UNITARY INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG𝓛

• Journal title : Honam Mathematical Journal
• Volume 36, Issue 4,  2014, pp.907-911
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2014.36.4.907
Title & Authors
UNITARY INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG𝓛
Kang, Joo Ho;

Abstract
Given vectors x and y in a separable complex Hilbert space $\small{\mathcal{H}}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following: Let $\small{Alg{\mathcal{L}}}$ be a tridiagonal algebra on $\small{\mathcal{H}}$ and let $\small{x=(x_i)}$ and $\small{y=(y_i)}$ be vectors in $\small{\mathcal{H}}$. Then the following are equivalent: (1) There exists a unitary operator $\small{A=(a_{ij})}$ in $\small{Alg{\mathcal{L}}}$ such that Ax = y. (2) There is a bounded sequence $\small{\{{\alpha}_i\}}$ in $\small{\mathbb{C}}$ such that $\small{{\mid}{\alpha}_i{\mid}=1}$ and $\small{y_i={\alpha}_ix_i}$ for $\small{i{\in}\mathbb{N}}$.
Keywords
unitary interpolation;CSL-algebra;tridiagonal algebra;$\small{Alg{\mathcal{L}}}$;
Language
English
Cited by
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