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A continuous model for quasinilpotent operators.

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Gallardo Gutiérrez, Eva A. and Partington, Jonathan R. and Rodriguez, Daniel J. (2016) A continuous model for quasinilpotent operators. Mathematische Zeitschrift . pp. 1-10. ISSN 0025-5874

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Official URL: http://link.springer.com/article/10.1007/s00209-016-1673-2


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Abstract

A classical result due to Foias and Pearcy establishes a discrete model for every quasinilpotent operator acting on a separable, infinite-dimensional complex Hilbert space HH . More precisely, given a quasinilpotent operator T on HH , there exists a compact quasinilpotent operator K in HH such that T is similar to a part of K⊕K⊕⋯⊕K⊕⋯K⊕K⊕⋯⊕K⊕⋯ acting on the direct sum of countably many copies of HH . We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0C0 -semigroups of quasinilpotent operators.


Item Type:Article
Uncontrolled Keywords:Quasinilpotent operators; C0-semigroup; Operator model; Entire function
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:38211
Deposited On:23 Jun 2016 08:26
Last Modified:24 Jun 2016 08:07

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