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Operator Theory and Indefinite Inner Product Spaces pp 299–335Cite as

A Functional Description for the Commutative WJ*-algebras of the D + κ -class

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 163))

Abstract

We consider the action in Krein spaces of weakly closed J-symmetric operator algebras with identity possessing an invariant maximal nonnegative subspace, presented as a direct sum of a finite-dimensional neutral subspace and a uniformly positive subspace. A relation between these algebras (that in addition are assumed to be commutative) and function spaces of the type L ∞ σ ∩ L 2 v is established.

This work was completed with the support of project CONICIT (Venezuela) No 97000668.

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Author information

Authors and Affiliations

  1. Department of Pure & Applied Mathematics, USB, Sartenejas-Baruta, Apartado 89.000, Caracas, 1080-A, Venezuela

    Vladimir Strauss

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  1. Vladimir Strauss
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow, G1 1XH, UK

    Matthias Langer

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10 / 101, 1040, Wien, Austria

    Annemarie Luger  & Harald Woracek  & 

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Dedicated to Professor Heinz Langer

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Strauss, V. (2005). A Functional Description for the Commutative WJ*-algebras of the D + κ -class. In: Langer, M., Luger, A., Woracek, H. (eds) Operator Theory and Indefinite Inner Product Spaces. Operator Theory: Advances and Applications, vol 163. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7516-7_13

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