Joint similarity and Integral operators on Bergman and Hardy spaces

Abstract

We show that every completely polynomially bounded operator is similar to a contraction and we consider the joint similarity problem for weighted Bergman shift operators .The similarity for polynomially bounded operators on Hilbert space are shown . The Hankel operators on Bergman spaces with similarity to contraction are established . We study joint similarity problems on vector-valued Bergman spaces and give two-sided estimates for approximation number of certain Volterra integral operators and Hardy-type operators in the essential Lebesgue space . We study the approximation numbers and Kolmogorov widths of Hardy-type operators in a non-homogeneous case and trees . We determined the remainder estimates for the approximation numbers of weighted Hardy operators acting on the Hilbert space . We construct the behaviour of the approximation numbers of Sobolev embedding and Bernstein widths in a nonhomogeneous case . We give some s-numbers to an integral operator on the Lebesgue space . Hence we give some results .