국가지식-학술정보
UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS
UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS
- 대한수학회
- Communications of the Korean Mathematical Society
- Vol.17 No.3
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2002.01487 - 493 (7 pages)
- 0
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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, ….
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