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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.11 No.2

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HILBERT-SCHMIDT INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALGL

HILBERT-SCHMIDT INTERPOLATION ON Ax = y IN ATRIDIAGONAL ALGEBRA ALGL

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2004, v.11 no.2, pp.167-173
Jo, Young-Soo (Department of Mathematics, Keimyung University)
Kang, Joo-Ho (Department of mathematics, Daegu University)
Jo, Young-Soo, & Kang, Joo-Ho. (2004). HILBERT-SCHMIDT INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALGL, 11(2), 167-173.

Abstract

Given vectors x and y in a separable Hilbert space $\cal H$, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate Hilbert-Schmidt interpolation problems for vectors in a tridiagonal algebra. We show the following: Let $\cal L$ be a subspace lattice acting on a separable complex Hilbert space $\cal H$ and let x = ($x_{i}$) and y = ($y_{i}$) be vectors in $\cal H$. Then the following are equivalent; (1) There exists a Hilbert-Schmidt operator A = ($a_{ij}$ in Alg$\cal L$ such that Ax = y. (2) There is a bounded sequence {$a_n$ in C such that ${\sum^{\infty}}_{n=1}\mid\alpha_n\mid^2 < \infty$ and $y_1 = \alpha_1x_1 + \alpha_2x_2$ ... $y_{2k} =\alpha_{4k-1}x_{2k}$ $y_{2k=1} = \alpha_{4kx2k} + \alpha_{4k+1}x_{2k+1} + \alpha_{4k+1}x_{2k+2}$ for K $\epsilon$ N.

keywords
Hilbert-Schmidt Interpolation, CSL-algebra, Tridiagonal algebra, AlgL

한국수학교육학회지시리즈B:순수및응용수학

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