• Title/Summary/Keyword: CSL-algebra

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UNITARY INTERPOLATION PROBLEMS IN CSL-ALGEBRA ALGL

  • Jo, Yong-Soo;Kang, Joo-Ho
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.2
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    • pp.207-213
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    • 2003
  • 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?

INVERTIBLE INTERPOLATION PROBLEMS IN CSL-ALGEBRA ALGL

  • Jo, Young-Soo;Kang, Joo-Ho
    • Journal of applied mathematics & informatics
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    • v.12 no.1_2
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    • pp.359-365
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    • 2003
  • Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. In this article, we investigate invertible interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H and x and y be vectors in H. When does there exist an invertible operator A in AlgL suth that An = ㅛ?

NORMAL INTERPOLATION PROBLEMS IN CSL-ALGEBRA ALG𝓛

  • JO, YOUNG SOO;KANG, JOO HO;PARK, DONG WAN
    • Honam Mathematical Journal
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    • v.27 no.3
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    • pp.431-443
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    • 2005
  • We investigate the equation Ax = y, where the vectors x and y are given and the operator A is normal and required to lie in CSL-algebra $AlG{\mathcal{L}}$. We desire a necessary and sufficient condition for the existence of a solution A.

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COMPACT INTERPOLATION FOR VECTORS IN TRIDIAGONAL ALGEBRA

  • Jo, Young-Soo;Kang, Joo-Ho
    • Communications of the Korean Mathematical Society
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    • v.18 no.3
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    • pp.485-490
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    • 2003
  • 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 $Tx_i=y_i$ , for i, = 1,2,…,n. In this article, we investigate compact interpolation problems in tridiagonal algebra : Given vectors x and y in a Hilbert space, when is there a compact operator A in a tridiagonal algebra such that Ax = y?

SELF-ADJOINT INTERPOLATION FOR VECTORS IN TRIDIAGONAL ALGEBRAS

  • Jo, Young-Soo
    • Journal of applied mathematics & informatics
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    • v.9 no.2
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    • pp.845-850
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    • 2002
  • Given vectors x and y in a filbert space H, an interpolating operator for vectors is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i=y_i$, for i = 1, 2 …, n. In this article, we investigate self-adjoint interpolation problems for vectors in tridiagonal algebra.

INTERPOLATION FOR HILBERT-SCHMIDT OPERATOR AND APPLICATION TO OPERATOR CORONA THEOREM

  • Kang, Joo-Ho;Ha, Dae-Yeon;Baik, Hyoung-Gu
    • Journal of applied mathematics & informatics
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    • v.9 no.1
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    • pp.341-347
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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 n-operators satisfies the equation $AX_i = Y_i$, for i = 1,2…, n. In this paper, we investigate Hilbert-Schmidt interpolation problems in tridiagonal algebra by connecting the classical corona theorem.

SELF-ADJOINT INTERPOLATION ON Ax = Y IN A TRIDIAGONAL ALGEBRA ALGL

  • PARK, DONGWAN;PARK, JAE HYUN
    • Honam Mathematical Journal
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    • v.28 no.1
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    • pp.135-140
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    • 2006
  • Given vectors x and y in a separable Hilbert space H, an interpolating operator is a bounded operator A such that Ax = y. In this article, we investigate self-adjoint interpolation problems for vectors in a tridiagonal algebra: Let AlgL be a tridiagonal algebra on a separable complex Hilbert space H and let $x=(x_i)$ and $y=(y_i)$ be vectors in H.Then the following are equivalent: (1) There exists a self-adjoint operator $A=(a_ij)$ in AlgL such that Ax = y. (2) There is a bounded real sequence {$a_n$} such that $y_i=a_ix_i$ for $i{\in}N$.

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COMPACT INTERPOLATION ON AX = Y IN A TRIDIAGONAL ALGEBRA ALGL

  • Kang, Joo-Ho
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.447-452
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    • 2005
  • Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

SELF-ADJOINT INTERPOLATION ON AX=Y IN A TRIDIAGONAL ALGEBRA ALG𝓛

  • Kang, Joo Ho;Lee, SangKi
    • Honam Mathematical Journal
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    • v.36 no.1
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    • pp.29-32
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    • 2014
  • Given operators X and Y acting on a separable Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate self-adjoint interpolation problems for operators in a tridiagonal algebra : Let $\mathcal{L}$ be a subspace lattice acting on a separable complex Hilbert space $\mathcal{H}$ and let X = ($x_{ij}$) and Y = ($y_{ij}$) be operators acting on $\mathcal{H}$. Then the following are equivalent: (1) There exists a self-adjoint operator A = ($a_{ij}$) in $Alg{\mathcal{L}}$ such that AX = Y. (2) There is a bounded real sequence {${\alpha}_n$} such that $y_{ij}={\alpha}_ix_{ij}$ for $i,j{\in}\mathbb{N}$.

UNITARY INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG𝓛

  • Kang, Joo Ho
    • Honam Mathematical Journal
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    • v.36 no.4
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    • pp.907-911
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    • 2014
  • Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax = y. We show the following: Let $Alg{\mathcal{L}}$ be a tridiagonal algebra on $\mathcal{H}$ and let $x=(x_i)$ and $y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a unitary operator $A=(a_{ij})$ in $Alg{\mathcal{L}}$ such that Ax = y. (2) There is a bounded sequence $\{{\alpha}_i\}$ in $\mathbb{C}$ such that ${\mid}{\alpha}_i{\mid}=1$ and $y_i={\alpha}_ix_i$ for $i{\in}\mathbb{N}$.