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

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

Cho, Ilwoo
Dutta, Hemen

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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. 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 previous theory showing how the Semicircular Law is deformed by actions from outside Explores free Hilbert Spaces and their modeling applications Authored by two leading researchers in Operator Theory and Operator Algebra INDICE: 1. Introduction 2. Free Hilbert Space 3. Jump Operators on Free Hilbert Spaces 4. Semicircular Elements Induced by a Free Hilbert Space 5. Jump Operators and Semicircularity 6. The Semicircular Law on LQ [H1,.,HN] 7. Shift Operators on Free Hilbert Spaces 8. Shift Operators and Semicircularity 9. Shift Operators Acting on LQ [H1,.,HN] 10. Jump-Shift Operators on Free Hilbert Spaces 11. Jump-Shift Operators and Semicircularity

  • ISBN: 978-0-443-15175-0
  • Editorial: Academic Press
  • Encuadernacion: Rústica
  • Fecha Publicación: 01/05/2023
  • Nº Volúmenes: 1
  • Idioma: Inglés