Remark on Lomonosov's lemma

Author:
W. E. Longstaff

Journal:
Proc. Amer. Math. Soc. **88** (1983), 311-312

MSC:
Primary 47A15

DOI:
https://doi.org/10.1090/S0002-9939-1983-0695264-3

MathSciNet review:
695264

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Abstract: The famous lemma of V. I. Lomonosov states that if is a transitive algebra of operators acting on a complex, infinite-dimensional Banach space and is a nonzero compact operator on , then there is an such that 1 is an eigenvalue of *AK*. Lomonosov's proof uses Schauder's fixed point theorem. A proof, using only elementary techniques, is given for the case where has finite-rank.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0695264-3

Article copyright:
© Copyright 1983
American Mathematical Society