Journal of Operator Theory

Operator Theory and Operator Algebras

On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

Operator and Spectral Theory

This lecture is a complete introduction to the general theory of operators on Hilbert spaces. We particularly focus on those tools that are essentials in Quantum Mechanics: unbounded operators, multiplication operators, self-adjointness, spectrum, functional calculus, spectral measures and von Neumann’s Spectral Theorem. 1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Multivariate Operator Theory

While the study of operator theory on Hilbert space has been underway for more than a hundred years, multivariate operator theory the study of more than one operator at a tim is of more recent origin. The study of self-adjoint algebras emerged in the late thirties in the works of Murray-von Neumann and Gelfand-Naimark. A couple of decades later, non self-adjoint algebras enjoyed considerable de...

Operator Probability Theory

This article presents an overview of some topics in operator probability theory. We do not strive for generality and only simple methods are employed. To give the reader a flavor of the subject we concentrate on the two most important topics, the law of large numbers and the central limit theorem.