Positive operators on Krein spaces View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1992-05

AUTHORS

Y. A. Abramovich, C. D. Aliprantis, O. Burkinshaw

ABSTRACT

A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace. More... »

PAGES

1-22

References to SciGraph publications

  • 1970. Ordered linear spaces in NONE
  • 1907-06. Zur Theorie der Matrices in MATHEMATISCHE ANNALEN
  • 1971. Topological Vector Spaces in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00046631

    DOI

    http://dx.doi.org/10.1007/bf00046631

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1011759394


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1701", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Psychology", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/17", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Psychology and Cognitive Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Indiana University \u2013 Purdue University Indianapolis", 
              "id": "https://www.grid.ac/institutes/grid.257413.6", 
              "name": [
                "Department of Mathematics, IUPUI, 46205, Indianapolis, IN, U.S.A"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Abramovich", 
            "givenName": "Y. A.", 
            "id": "sg:person.013761237533.23", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013761237533.23"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Indiana University \u2013 Purdue University Indianapolis", 
              "id": "https://www.grid.ac/institutes/grid.257413.6", 
              "name": [
                "Department of Mathematics, IUPUI, 46205, Indianapolis, IN, U.S.A"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Aliprantis", 
            "givenName": "C. D.", 
            "id": "sg:person.014135050231.02", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014135050231.02"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Indiana University \u2013 Purdue University Indianapolis", 
              "id": "https://www.grid.ac/institutes/grid.257413.6", 
              "name": [
                "Department of Mathematics, IUPUI, 46205, Indianapolis, IN, U.S.A"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Burkinshaw", 
            "givenName": "O.", 
            "id": "sg:person.011747227346.83", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011747227346.83"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bfb0059130", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011122270", 
              "https://doi.org/10.1007/bfb0059130"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0059130", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011122270", 
              "https://doi.org/10.1007/bfb0059130"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01449896", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036747242", 
              "https://doi.org/10.1007/bf01449896"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4684-9928-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038819455", 
              "https://doi.org/10.1007/978-1-4684-9928-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4684-9928-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038819455", 
              "https://doi.org/10.1007/978-1-4684-9928-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/memo/0024", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059343073"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1992-05", 
        "datePublishedReg": "1992-05-01", 
        "description": "A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf00046631", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1028030", 
            "issn": [
              "0167-8019", 
              "1572-9036"
            ], 
            "name": "Acta Applicandae Mathematicae", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1-2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "27"
          }
        ], 
        "name": "Positive operators on Krein spaces", 
        "pagination": "1-22", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "380716b99d6434350e8bf5934fd49757fe9cd6222568b667a1b8ec4cb85a18ed"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf00046631"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1011759394"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf00046631", 
          "https://app.dimensions.ai/details/publication/pub.1011759394"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T13:57", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000371_0000000371/records_130820_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/BF00046631"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf00046631'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf00046631'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00046631'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00046631'


     

    This table displays all metadata directly associated to this object as RDF triples.

    90 TRIPLES      21 PREDICATES      31 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf00046631 schema:about anzsrc-for:17
    2 anzsrc-for:1701
    3 schema:author N69c75423fbf8466c82a71448fb22b18b
    4 schema:citation sg:pub.10.1007/978-1-4684-9928-5
    5 sg:pub.10.1007/bf01449896
    6 sg:pub.10.1007/bfb0059130
    7 https://doi.org/10.1090/memo/0024
    8 schema:datePublished 1992-05
    9 schema:datePublishedReg 1992-05-01
    10 schema:description A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.
    11 schema:genre research_article
    12 schema:inLanguage en
    13 schema:isAccessibleForFree false
    14 schema:isPartOf N126aead8917c4cc0b38e06861a7a3100
    15 N5cb4ec33be4e410b852b052d12cbe179
    16 sg:journal.1028030
    17 schema:name Positive operators on Krein spaces
    18 schema:pagination 1-22
    19 schema:productId N39d6b42275f64016a88b631f6fb46613
    20 N7557781f56e3428db806bccd9cf7aeb4
    21 N98f64741554744369d682371d30c2160
    22 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011759394
    23 https://doi.org/10.1007/bf00046631
    24 schema:sdDatePublished 2019-04-11T13:57
    25 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    26 schema:sdPublisher N6afc812b986547a08baf298f32f71369
    27 schema:url http://link.springer.com/10.1007/BF00046631
    28 sgo:license sg:explorer/license/
    29 sgo:sdDataset articles
    30 rdf:type schema:ScholarlyArticle
    31 N126aead8917c4cc0b38e06861a7a3100 schema:issueNumber 1-2
    32 rdf:type schema:PublicationIssue
    33 N39d6b42275f64016a88b631f6fb46613 schema:name doi
    34 schema:value 10.1007/bf00046631
    35 rdf:type schema:PropertyValue
    36 N4d27a01cacd344a5a9db9041ca91bd76 rdf:first sg:person.014135050231.02
    37 rdf:rest Nbf47fbceab814490ad7dd931a221fe56
    38 N5cb4ec33be4e410b852b052d12cbe179 schema:volumeNumber 27
    39 rdf:type schema:PublicationVolume
    40 N69c75423fbf8466c82a71448fb22b18b rdf:first sg:person.013761237533.23
    41 rdf:rest N4d27a01cacd344a5a9db9041ca91bd76
    42 N6afc812b986547a08baf298f32f71369 schema:name Springer Nature - SN SciGraph project
    43 rdf:type schema:Organization
    44 N7557781f56e3428db806bccd9cf7aeb4 schema:name dimensions_id
    45 schema:value pub.1011759394
    46 rdf:type schema:PropertyValue
    47 N98f64741554744369d682371d30c2160 schema:name readcube_id
    48 schema:value 380716b99d6434350e8bf5934fd49757fe9cd6222568b667a1b8ec4cb85a18ed
    49 rdf:type schema:PropertyValue
    50 Nbf47fbceab814490ad7dd931a221fe56 rdf:first sg:person.011747227346.83
    51 rdf:rest rdf:nil
    52 anzsrc-for:17 schema:inDefinedTermSet anzsrc-for:
    53 schema:name Psychology and Cognitive Sciences
    54 rdf:type schema:DefinedTerm
    55 anzsrc-for:1701 schema:inDefinedTermSet anzsrc-for:
    56 schema:name Psychology
    57 rdf:type schema:DefinedTerm
    58 sg:journal.1028030 schema:issn 0167-8019
    59 1572-9036
    60 schema:name Acta Applicandae Mathematicae
    61 rdf:type schema:Periodical
    62 sg:person.011747227346.83 schema:affiliation https://www.grid.ac/institutes/grid.257413.6
    63 schema:familyName Burkinshaw
    64 schema:givenName O.
    65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011747227346.83
    66 rdf:type schema:Person
    67 sg:person.013761237533.23 schema:affiliation https://www.grid.ac/institutes/grid.257413.6
    68 schema:familyName Abramovich
    69 schema:givenName Y. A.
    70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013761237533.23
    71 rdf:type schema:Person
    72 sg:person.014135050231.02 schema:affiliation https://www.grid.ac/institutes/grid.257413.6
    73 schema:familyName Aliprantis
    74 schema:givenName C. D.
    75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014135050231.02
    76 rdf:type schema:Person
    77 sg:pub.10.1007/978-1-4684-9928-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038819455
    78 https://doi.org/10.1007/978-1-4684-9928-5
    79 rdf:type schema:CreativeWork
    80 sg:pub.10.1007/bf01449896 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036747242
    81 https://doi.org/10.1007/bf01449896
    82 rdf:type schema:CreativeWork
    83 sg:pub.10.1007/bfb0059130 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011122270
    84 https://doi.org/10.1007/bfb0059130
    85 rdf:type schema:CreativeWork
    86 https://doi.org/10.1090/memo/0024 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059343073
    87 rdf:type schema:CreativeWork
    88 https://www.grid.ac/institutes/grid.257413.6 schema:alternateName Indiana University – Purdue University Indianapolis
    89 schema:name Department of Mathematics, IUPUI, 46205, Indianapolis, IN, U.S.A
    90 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...