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ArticleOriginal scientific text

Title

Invariant subspaces and spectral mapping theorems

Authors 1

Affiliations

  1. Department of Mathematics, Vologda Polytechnical Institute, 15 Lenin St., 160008 Vologda, Russia

Abstract

We discuss some results and problems connected with estimation of spectra of operators (or elements of general Banach algebras) which are expressed as polynomials in several operators, noncommuting but satisfying weaker conditions of commutativity type (for example, generating a nilpotent Lie algebra). These results have applications in the theory of invariant subspaces; in fact, such applications were the motivation for consideration of spectral problems. More or less detailed proofs are given for results unpublished before or published in short communications; in some other cases we give a scheme of proof. The author is obliged to J. A. Erdos, V. S. Guba and especially to Yu. V. Turovskiĭ for useful discussions.

Bibliography

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Banach Center Publications
1994/30/1
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Pages:
313-325
Main language of publication
English
Published
1994
Exact and natural sciences