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UNITARY INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG𝓛

  • Kang, Joo Ho (Dept. of Math., Daegu University)
  • Received : 2014.11.06
  • Accepted : 2014.11.19
  • Published : 2014.12.25

Abstract

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

Keywords

unitary interpolation;CSL-algebra;tridiagonal algebra;$Alg{\mathcal{L}}$

Acknowledgement

Supported by : Daegu University

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