• Title, Summary, Keyword: Alg(equation omitted)

### INVERTIBLE INTERPOLATION PROBLEMS IN ALG(equation omitted)

• Jo, Young-Soo
• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.319-326
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• 2004
• In this article, we investigate invertible interpolation problems in Alg(equation omitted) : Let(equation omitted) be a subspace lattice on a Hilbert space H and let X and Y be operators acting on H. When does there exist an invertible operator A in Alg(equation omitted) such that AX = Y?

### NORMAL INTERPOLATION PROBLEMS IN ALGL

• Jo, Young-Soo
• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.691-700
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• 2004
• Let X and Y be operators acting on a Hilbert space and let (equation omitted) be a subspace lattice of orthogonal projections on the space containing 0 and I. We investigate normal interpolation problems in Alg(equation omitted): Given operators X and Y acting on a Hilbert space, when does there exist a normal operator A in Alg(equation omitted) such that AX = Y?

### ON OPERATOR INTERPOLATION PROBLEMS

• Jo, Young-Soo;Kang, Joo-Ho;Kim, Ki-Sook
• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.423-433
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• 2004
• In this paper we obtained the following: Let H. be a Hilbert space and (equation omitted) be a subspace lattice on H. Let X and Y be operators acting on H. If the range of X is dense in H, then the following are equivalent: (1) there exists an operator A in Alg(equation omitted) such that AX = Y, (2) sup (equation omitted) Moreover, if condition (2) holds, we may choose the operator A such that ∥A∥ = K.

### UNITARY INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

• Kang, Joo-Ho;Jo, Young-Soo
• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.487-493
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• 2002

### Self-Adjoint Interpolation Problems in ALGL

• 강주호;조영수
• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• pp.4.1-4
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• 2003
• 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 n-operators satisfies the equation AXi= Yi, for i = 1,2,...,n, In this article, we showed the following : Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that rangeX is dense in H. Then the following statements are equivalent : (1) There exists an operator A in AlgL such that AX = Y, A$\^$*/=A and every E in L reduces A. (2) sup｛(equation omitted) : n $\in$ N f$\sub$I/ $\in$ H and E$\sub$I/ $\in$ L｝<$\infty$ and = for all E in L and all f, g in H.