UNITARY INTERPOLATION PROBLEMS IN CSL-ALGEBRA ALGL

• Jo, Yong-Soo (Department of Mathematics, Keimyung University) ;
• Kang, Joo-Ho (Department of Mathematics, Taegu University)
• Published : 2003.05.01

Abstract

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. An interpolating operator for n-vectors satisfies the equation Ax$_{i}$=y$_{i}$. for i=1,2, …, n. In this article, we investigate unitary interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H. Let x and y be vectors in H. When does there exist a unitary operator A in AlgL such that Ax=y?

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