On principal T-bands in a Banach lattice View Full Text


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Article Info

DATE

1997-12

AUTHORS

J J Grobler, C J Reinecke

ABSTRACT

It is shown that for every positive order continuous Riesz operatorT, defined on an order complete complex Banach latticeE which is separated by its Köthe dual, there exists a Frobenius decomposition ofE into a countable number of disjoint principalT-bands and a band on whichT is quasi-nilpotent. A basis for the generalized eigenspace ofT pertaining to its maximal eigenvalue is constructed and the positivity properties of its elements are studied. The distinguished eigenvalues ofT are characterized and it is also shown that the theory ofT-bands is symmetric with respect to the duality which exists betweenE and its Köthe dual. This generalizes aspects of work done by H.D. Victory and R.-J. Jang-Lewis. More... »

PAGES

444-465

References to SciGraph publications

  • 1995. Spectral Theory in Banach Lattices in OPERATOR THEORY IN FUNCTION SPACES AND BANACH LATTICES
  • 1991. Banach Lattices in NONE
  • 1974. Banach Lattices and Positive Operators in NONE
  • 1986-03. Irreducible compact operators in MATHEMATISCHE ZEITSCHRIFT
  • 1968-02. Über das Spektrum positiver Operatoren in MATHEMATISCHE ZEITSCHRIFT
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01309156

    DOI

    http://dx.doi.org/10.1007/bf01309156

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1003547975


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