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Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law Cho, Ilwoo (Professor Department of Mathematics and Statistics, St. Ambrose University, USA)
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Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law
Cho, Ilwoo (Professor Department of Mathematics and Statistics, St. Ambrose University, USA)
In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider 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.
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300 pages
| Media | Books Paperback Book (Book with soft cover and glued back) |
| Released | April 26, 2023 |
| ISBN13 | 9780443151750 |
| Publishers | Elsevier Science Publishing Co Inc |
| Pages | 164 |
| Dimensions | 234 × 189 × 13 mm · 294 g |
| Language | English |
