Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law (Paperback) (ISBN-13: 9780443151750)

In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l² 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.

Author: Ilwoo Cho, Hemen Dutta
ISBN-10: 044315175X
ISBN-13: 9780443151750
Publisher: Academic Press
Language: English
Published: 04/26/2023
Pages: 164
Format: Paperback
Weight: 0.65lbs
Size: 9.25h x 7.50w x 0.35d