Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law

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ISBN: 9780443151750
Author : Hemen Dutta
Published: 2023
Publisher: Academic Press
Language: English
Format: Paperback / softback
Format: 9.25×7.5

Description

In <i>Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law</i>, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l<SUP>2</SUP> Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how “free-Hilbert-space Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how “inside actions of operator algebra deform the free-probabilistic information—in particular, the semicircular law.

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