• Title, Summary, Keyword: tridiagonal algebra

### 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 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 $i{\in}N$.

### INTERPOLATION PROBLEMS FOR INFINITE DIMENSIONAL TRIDIAGONAL ALGEBRA Alg𝓛∞

• CHOI, TAEG-YOUNG;SONG, YEUNG-GUY;PARK, YONG-KIL
• Honam Mathematical Journal
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• v.27 no.1
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• pp.83-100
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• 2005

### COMPACT INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALG$\mathcal{L}$

• Kang, Joo-Ho
• Honam Mathematical Journal
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• v.32 no.2
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• pp.255-260
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• 2010
• 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. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. We show the following : Let Alg$\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let x = $(x_i)$ and y = $(y_i)$ be vectors in H. Then the following are equivalent: (1) There exists a compact operator A = $(a_{ij})$ in Alg$\mathcal{L}$ such that Ax = y. (2) There is a sequence ${{\alpha}_n}$ in $\mathbb{C}$ such that ${{\alpha}_n}$ converges to zero and for all k ${\in}$ $\mathbb{N}$, $y_1 = {\alpha}_1x_1 + {\alpha}_2x_2$ $y_{2k} = {\alpha}_{4k-1}x_{2k}$ $y_{2k+1}={\alpha}_{4k}x_{2k}+{\alpha}_{4k+1}x_{2k+1}+{\alpha}_{4k+2}+x_{2k+2}$.

### 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 $i{\in}\mathbb{N}$.