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Sublinearity and Other Spectral Conditions on a Semigroup

Published online by Cambridge University Press:  20 November 2018

Heydar Radjavi
Heydar Radjavi*
Affiliation:
Dalhousie University, Halifax, Nova Scotia, B3H 3J5
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Abstract

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Subadditivity, sublinearity, submultiplicativity, and other conditions are considered for spectra of pairs of operators on a Hilbert space. Sublinearity, for example, is a weakening of the well-known property $L$ and means $\sigma (A\,+\,\lambda B)\,\subseteq \,\sigma (A)\,+\,\lambda \sigma (B)$ for all scalars $\lambda$. The effect of these conditions is examined on commutativity, reducibility, and triangularizability of multiplicative semigroups of operators. A sample result is that sublinearity of spectra implies simultaneous triangularizability for a semigroup of compact operators.

Keywords

47A1547D0315A3020A2047A1047B10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 1 , 01 February 2000 , pp. 197 - 224
Copyright
Copyright © Canadian Mathematical Society 2000

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