# TRACE-CLASS INTERPOLATION FOR VECTORS IN TRIDIAGONAL ALGEBRAS

• Jo, Young-Soo (Department of Mathematics, Keimyung University) ;
• Kang, Joo-Ho (Department of Mathematics, Taegu University)
• Published : 2002.02.01
• 117 7

#### Abstract

Given vectors x and y in a Hilbert space, an intepolating operator is a bounded operator T such that Tx=y. an interpolating operator for n vectors satisfies the equation Tx$_{i}$=y, for i=1, 2,…, n. In this article, we obtained the fellowing : Let x = (x$_{i}$) and y = (y$_{i}$) be two vectors in H such that x$_{i}$$\neq$0 for all i = 1, 2,…. Then the following statements are equivalent. (1) There exists an operator A in AlgＬ such that Ax = y, A is a trace-class operator and every E in Ｌ reduces A. (2) (equation omitted).mitted).

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