UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

Title & Authors
UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS
Kang, Joo-Ho; Jo, Young-Soo;

Abstract
Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for the n-operators satisfies the equation AX$\small{\_}$i/ : Y$\small{\_}$i/, for i = 1, 2 …, n. In this article, we obtained the following : Let X = (x$\small{\_}$ij/) and Y = (y$\small{\_}$ij/) be operators acting on H such that $\small{\varkappa}$$\small{\_}$ i$\small{\sigma}$ (i)/ 0 for all i. Then the following statements are equivalent. (1) There exists a unitary operator A in Alg(equation omitted) such that AX = Y and every E in (equation omitted) reduces A. (2) sup{(equation omitted)}<$\small{\infty}$ and (equation omitted) = 1 for all i = 1, 2, ….
Keywords
interpolation problem;subspace lattice;unitary interpolation problem;Alg(equation omitted);
Language
English
Cited by
References
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