Joint Spectral Radius, Operator Semigroups, and a Problem of W. Wojtyski

Authors: Shulman V.S.¹; Turovski breve inodot Y.V.²

Source: Journal of Functional Analysis, Volume 177, Number 2, November 2000 , pp. 383-441(59)

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Abstract:

We investigate the connections between the invariant subspace problem for operator semigroups and the joint spectral radius. As a consequence, it is proved that any quasinilpotent Lie algebra of compact operators on a Banach space is triangularizable. We extend the Berger–Wang formula to precompact sets of essentially scalar operators and prove the continuity of the joint spectral radius on them. Copyright 2000 Academic Press.

Keywords: joint spectral radius; semigroup; Lie algebra; invariant subspace

Language: English

Document Type: Research article

Affiliations: 1: School of Computing Technology and Mathematical Sciences, University of North London, 166-200 Holloway Road, London NO7 8DB, England 2: Institute of Mathematics and Mechanics of Academy of Sciences of Azerbaijan, F. Agaev str. 9, Baku, 370141, Azerbaijan

Publication date: 2000-11-01