Toeplitz Operators of Bergman Spaces and Non-Vanishing Functions on Bounded Symmetric Domains of Tube-Type

Abstract

We study Poisson itegerals and boundary components with a realization of Riemannian symmetric spaces. The Toeplitz matrices, unitary equivalence, 𝐿𝑝-isometries , equimeasurability , topological and analytical indices in C*-algebras are considered. We show the Toeplitz operators, rational inner functions, boundary value problems for the Shilov boundary, isometries and Toeplitz operators of Bergman space of bounded symmetric domains with a non-vanishing functions and Toeplitz operators on tube-type domains. We introduce the similarity equivalence of Toeplitz operators with the index of several complex variables and index theorem on the quarter-plane.