Interpolation Problems for Trace-Class Operator in Tridiagonal Algebra

Abstract

Given operators X and Y in a Hilbert space, an interpolating operator is a bounded operator T such that TX=Y. In this article, we obtained the following: Let X=(x_i,j) and Y=(y_i,j) be operators in B(H) such that s_iσ(i) 0 for all i where σ:N->N is a mapping. Then the following statements are equivalent. (1) There exists an operator A in AlgL such that AX=Y, every E in L reduces A and A is a trace-class operator. (2) .