Extension Theorems for Contraction Operators on Kreĭn Spaces View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1990

AUTHORS

Michael A. Dritschel , James Rovnyak

ABSTRACT

Notions of Julia and defect operators are used as a foundation for a theory of matrix extension and commutant lifting problems for contraction operators on Kreĭn spaces. The account includes a self-contained treatment of key propositions from the theory of Potapov, Ginsburg, Kreĭn, and Shmul’yan on the behavior of a contraction operator on negative subspaces. This theory is extended by an analysis of the behavior of the adjoint of a contraction operator on negative subspaces. Together, these results provide the technical input for the main extension theorems. More... »

PAGES

221-305

References to SciGraph publications

  • 1988-01. Lifting intertwining relations in INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Book

    TITLE

    Extension and Interpolation of Linear Operators and Matrix Functions

    ISBN

    978-3-7643-2530-5
    978-3-0348-7701-5

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-0348-7701-5_5

    DOI

    http://dx.doi.org/10.1007/978-3-0348-7701-5_5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1026233832


    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/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Purdue University", 
              "id": "https://www.grid.ac/institutes/grid.169077.e", 
              "name": [
                "Department of Mathematics Mathematical Sciences Building, Purdue University, West Lafayette, Indiana\u00a047907, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Dritschel", 
            "givenName": "Michael A.", 
            "id": "sg:person.010707720201.35", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010707720201.35"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Virginia", 
              "id": "https://www.grid.ac/institutes/grid.27755.32", 
              "name": [
                "Department of Mathematics Mathematics-Astronomy Building, University of Virginia, Charlottesville, Virginia\u00a022903, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rovnyak", 
            "givenName": "James", 
            "id": "sg:person.01351714224.63", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01351714224.63"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1017/s0013091500028418", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015900152"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01236657", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025530169", 
              "https://doi.org/10.1007/bf01236657"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01236657", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025530169", 
              "https://doi.org/10.1007/bf01236657"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1990", 
        "datePublishedReg": "1990-01-01", 
        "description": "Notions of Julia and defect operators are used as a foundation for a theory of matrix extension and commutant lifting problems for contraction operators on Kre\u012dn spaces. The account includes a self-contained treatment of key propositions from the theory of Potapov, Ginsburg, Kre\u012dn, and Shmul\u2019yan on the behavior of a contraction operator on negative subspaces. This theory is extended by an analysis of the behavior of the adjoint of a contraction operator on negative subspaces. Together, these results provide the technical input for the main extension theorems.", 
        "editor": [
          {
            "familyName": "Gohberg", 
            "givenName": "I.", 
            "type": "Person"
          }
        ], 
        "genre": "chapter", 
        "id": "sg:pub.10.1007/978-3-0348-7701-5_5", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": {
          "isbn": [
            "978-3-7643-2530-5", 
            "978-3-0348-7701-5"
          ], 
          "name": "Extension and Interpolation of Linear Operators and Matrix Functions", 
          "type": "Book"
        }, 
        "name": "Extension Theorems for Contraction Operators on Kre\u012dn Spaces", 
        "pagination": "221-305", 
        "productId": [
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/978-3-0348-7701-5_5"
            ]
          }, 
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "7cf9f43619624270b337a5fb67dbd009e581551b6f054c590dff25afc0836720"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1026233832"
            ]
          }
        ], 
        "publisher": {
          "location": "Basel", 
          "name": "Birkh\u00e4user Basel", 
          "type": "Organisation"
        }, 
        "sameAs": [
          "https://doi.org/10.1007/978-3-0348-7701-5_5", 
          "https://app.dimensions.ai/details/publication/pub.1026233832"
        ], 
        "sdDataset": "chapters", 
        "sdDatePublished": "2019-04-15T18:11", 
        "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/v90/0000000001_0000000264/records_8681_00000259.jsonl", 
        "type": "Chapter", 
        "url": "http://link.springer.com/10.1007/978-3-0348-7701-5_5"
      }
    ]
     

    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.10.1007/978-3-0348-7701-5_5'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-7701-5_5'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-7701-5_5'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-0348-7701-5_5'


     

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

    82 TRIPLES      23 PREDICATES      29 URIs      20 LITERALS      8 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/978-3-0348-7701-5_5 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nd61a1bf587c8402985303f33a61893ca
    4 schema:citation sg:pub.10.1007/bf01236657
    5 https://doi.org/10.1017/s0013091500028418
    6 schema:datePublished 1990
    7 schema:datePublishedReg 1990-01-01
    8 schema:description Notions of Julia and defect operators are used as a foundation for a theory of matrix extension and commutant lifting problems for contraction operators on Kreĭn spaces. The account includes a self-contained treatment of key propositions from the theory of Potapov, Ginsburg, Kreĭn, and Shmul’yan on the behavior of a contraction operator on negative subspaces. This theory is extended by an analysis of the behavior of the adjoint of a contraction operator on negative subspaces. Together, these results provide the technical input for the main extension theorems.
    9 schema:editor N9fcd838e421f4dc1b83cc4cd11d5bf66
    10 schema:genre chapter
    11 schema:inLanguage en
    12 schema:isAccessibleForFree false
    13 schema:isPartOf N9cfe708ff31a4ffc94a30d3bc3d43e65
    14 schema:name Extension Theorems for Contraction Operators on Kreĭn Spaces
    15 schema:pagination 221-305
    16 schema:productId N09e1c28a51134d12a1b0f2a0c8d18f10
    17 N620b1a4043984dfd8a5df371c76f4ead
    18 Ndb81d6b586b44c6fbbdd5f5819ec6277
    19 schema:publisher Ncf4c041c8f344b5180aecc804328ee41
    20 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026233832
    21 https://doi.org/10.1007/978-3-0348-7701-5_5
    22 schema:sdDatePublished 2019-04-15T18:11
    23 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    24 schema:sdPublisher Nd25b2d58d22e4c84b13a174021cf4981
    25 schema:url http://link.springer.com/10.1007/978-3-0348-7701-5_5
    26 sgo:license sg:explorer/license/
    27 sgo:sdDataset chapters
    28 rdf:type schema:Chapter
    29 N09e1c28a51134d12a1b0f2a0c8d18f10 schema:name dimensions_id
    30 schema:value pub.1026233832
    31 rdf:type schema:PropertyValue
    32 N60e176c8dbe648f297c3c4fd01e8b0b0 rdf:first sg:person.01351714224.63
    33 rdf:rest rdf:nil
    34 N620b1a4043984dfd8a5df371c76f4ead schema:name readcube_id
    35 schema:value 7cf9f43619624270b337a5fb67dbd009e581551b6f054c590dff25afc0836720
    36 rdf:type schema:PropertyValue
    37 N7ad9a01e111a468b971057a2f2e6d638 schema:familyName Gohberg
    38 schema:givenName I.
    39 rdf:type schema:Person
    40 N9cfe708ff31a4ffc94a30d3bc3d43e65 schema:isbn 978-3-0348-7701-5
    41 978-3-7643-2530-5
    42 schema:name Extension and Interpolation of Linear Operators and Matrix Functions
    43 rdf:type schema:Book
    44 N9fcd838e421f4dc1b83cc4cd11d5bf66 rdf:first N7ad9a01e111a468b971057a2f2e6d638
    45 rdf:rest rdf:nil
    46 Ncf4c041c8f344b5180aecc804328ee41 schema:location Basel
    47 schema:name Birkhäuser Basel
    48 rdf:type schema:Organisation
    49 Nd25b2d58d22e4c84b13a174021cf4981 schema:name Springer Nature - SN SciGraph project
    50 rdf:type schema:Organization
    51 Nd61a1bf587c8402985303f33a61893ca rdf:first sg:person.010707720201.35
    52 rdf:rest N60e176c8dbe648f297c3c4fd01e8b0b0
    53 Ndb81d6b586b44c6fbbdd5f5819ec6277 schema:name doi
    54 schema:value 10.1007/978-3-0348-7701-5_5
    55 rdf:type schema:PropertyValue
    56 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    57 schema:name Mathematical Sciences
    58 rdf:type schema:DefinedTerm
    59 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    60 schema:name Pure Mathematics
    61 rdf:type schema:DefinedTerm
    62 sg:person.010707720201.35 schema:affiliation https://www.grid.ac/institutes/grid.169077.e
    63 schema:familyName Dritschel
    64 schema:givenName Michael A.
    65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010707720201.35
    66 rdf:type schema:Person
    67 sg:person.01351714224.63 schema:affiliation https://www.grid.ac/institutes/grid.27755.32
    68 schema:familyName Rovnyak
    69 schema:givenName James
    70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01351714224.63
    71 rdf:type schema:Person
    72 sg:pub.10.1007/bf01236657 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025530169
    73 https://doi.org/10.1007/bf01236657
    74 rdf:type schema:CreativeWork
    75 https://doi.org/10.1017/s0013091500028418 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015900152
    76 rdf:type schema:CreativeWork
    77 https://www.grid.ac/institutes/grid.169077.e schema:alternateName Purdue University
    78 schema:name Department of Mathematics Mathematical Sciences Building, Purdue University, West Lafayette, Indiana 47907, USA
    79 rdf:type schema:Organization
    80 https://www.grid.ac/institutes/grid.27755.32 schema:alternateName University of Virginia
    81 schema:name Department of Mathematics Mathematics-Astronomy Building, University of Virginia, Charlottesville, Virginia 22903, USA
    82 rdf:type schema:Organization
     




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


    ...