"The present monograph considers semicircular elements whose free distributions are the semicircular law induced by some mutually orthogonal projections on the free Hilbert space induced by fixed multi Hilbert spaces…. This motivates the authors of the present monograph to introduce certain operators which preserve or distort the semicircular law.... The book will be interesting and useful for mathematicians working in this area." --Ali Talebi, zbMATHOpen
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.
Les mer
1. Fundamentals
2. Semicircular Elements Induced by Orthogonal Projections
3. Semicircular Elements Induced by Projections On l2-Spaces
4. Jump Operators on Free Hilbert Spaces and Deformed Semicircular Laws
5. Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws
6. Jump-Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws
Les mer
"The present monograph considers semicircular elements whose free distributions are the semicircular law induced by some mutually orthogonal projections on the free Hilbert space induced by fixed multi Hilbert spaces…. This motivates the authors of the present monograph to introduce certain operators which preserve or distort the semicircular law.... The book will be interesting and useful for mathematicians working in this area." --Ali Talebi, zbMATHOpen
Les mer
Presents the construction of free Hilbert-Space Operators and how they affect the Semicircular Law
Presents the spectral properties of three types of operators on a Hilbert space, in particular how these operators affect the semicircular law
Demonstrates how the semicircular law is deformed by actions "from inside", as opposed to actions "from outside" considered by previous theory
Explores free Hilbert spaces and their modeling applications
Authored by two leading researchers in Operator Theory and Operator Algebra
Les mer
Produktdetaljer
ISBN
9780443151750
Publisert
2023-04-26
Utgiver
Vendor
Academic Press Inc
Vekt
450 gr
Høyde
235 mm
Bredde
191 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
164