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

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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
  • 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, ….

SKEW-ADJOINT INTERPOLATION ON Ax-y IN $ALG\mathcal{L}$

  • Jo, Young-Soo;Kang, Joo-Ho
    • The Pure and Applied Mathematics
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    • v.11 no.1
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    • pp.29-36
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    • 2004
  • Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and y be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

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TRACE-CLASS INTERPOLATION FOR VECTORS IN TRIDIAGONAL ALGEBRAS

  • Jo, Young-Soo;Kang, Joo-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.63-69
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    • 2002
  • Given vectors x and y in a Hilbert space, an intepolating operator is a bounded operator T such that Tx=y. an interpolating operator for n vectors satisfies the equation Tx$_{i}$=y, for i=1, 2,…, n. In this article, we obtained the fellowing : Let x = (x$_{i}$) and y = (y$_{i}$) be two vectors in H such that x$_{i}$$\neq$0 for all i = 1, 2,…. Then the following statements are equivalent. (1) There exists an operator A in AlgL such that Ax = y, A is a trace-class operator and every E in L reduces A. (2) (equation omitted).mitted).

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.

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