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 considers so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and the operators acting on them. The book discusses their construction, considers spectral-theoretic properties of these operators, illustrate how "free-Hilbert-space? Operator Theory is different from the classical Operator Theory, and 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.