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On Jordan ideals and submodules: Algebraic and analytic aspects

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Abstract

Let

be an algebra, and let X be an arbitrary

-bimodule. A linear space Y ⊂ X is called a Jordan

-submodule if Ay + yA ∈ Y for all A ∈

and y ∈ Y. (For X =

, this coincides with the notion of a Jordan ideal.) We study conditions under which Jordan submodules are subbimodules. General criteria are given in the purely algebraic situation as well as for the case of Banach bimodules over Banach algebras. We also consider symmetrically normed Jordan submodules over C*-algebras. It turns out that there exist C*-algebras in which not all Jordan ideals are ideals.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Maribor, Maribor, Yugoslavia

    M. Brešar

  2. Department of Computing, Communication Technology and Mathematics, London Metropolitan University, London, UK

    E. V. Kissin

  3. Department of Higher Mathematics, Vologda Technical University, Vologda, Russia

    V. S. Shulman

Authors
  1. M. Brešar
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  2. E. V. Kissin
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  3. V. S. Shulman
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Corresponding author

Correspondence to M. Brešar.

Additional information

__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 42, No. 3, pp. 71–75, 2008

Original Russian Text Copyright © by M. Brešar, E. V. Kissin, and V. S. Shulman

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Brešar, M., Kissin, E.V. & Shulman, V.S. On Jordan ideals and submodules: Algebraic and analytic aspects. Funct Anal Its Appl 42, 220–223 (2008). https://doi.org/10.1007/s10688-008-0031-5

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  • DOI: https://doi.org/10.1007/s10688-008-0031-5

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