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UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

  • Kang, Joo-Ho (Department of Mathematics Taegu University) ;
  • Jo, Young-Soo (Department of Mathematic Keimyung University)
  • Published : 2002.07.01

Abstract

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for the n-operators satisfies the equation AX$\_$i/ : Y$\_$i/, for i = 1, 2 …, n. In this article, we obtained the following : Let X = (x$\_$ij/) and Y = (y$\_$ij/) be operators acting on H such that $\varkappa$$\_$ i$\sigma$ (i)/ 0 for all i. Then the following statements are equivalent. (1) There exists a unitary operator A in Alg(equation omitted) such that AX = Y and every E in (equation omitted) reduces A. (2) sup{(equation omitted)}<$\infty$ and (equation omitted) = 1 for all i = 1, 2, ….

Keywords

interpolation problem;subspace lattice;unitary interpolation problem;Alg(equation omitted)

References

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