TRACE-CLASS INTERPOLATION FOR VECTORS IN TRIDIAGONAL ALGEBRAS

Title & Authors
TRACE-CLASS INTERPOLATION FOR VECTORS IN TRIDIAGONAL ALGEBRAS
Jo, Young-Soo; Kang, Joo-Ho;

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$\small{_{i}}$=y, for i=1, 2,…, n. In this article, we obtained the fellowing : Let x = (x$\small{_{i}}$) and y = (y$\small{_{i}}$) be two vectors in H such that x$\small{_{i}}$$\small{\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).
Keywords
trace-class;tridiagonal algebra;commutative subspace lattice;AlgＬ;
Language
English
Cited by
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