• Title, Summary, Keyword: tridiagonal algebras

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ISOMETRIES OF (2)}_{2n}$

  • Park, Taeg-Young
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.609-620
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    • 1995
  • In this paper, we introduce the generalization $A^{(2)}_{2n}$ of tridiagonal algebras $A_{2n}$ and investigate the isometries of such algebras.

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Isometries of $B_{2n - (T_0)}

  • Park, Taeg-Young
    • Journal of the Korean Mathematical Society
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    • v.32 no.3
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    • pp.593-608
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    • 1995
  • The study of self-adjoint operator algebras on Hilbert space is well established, with a long history including some of the strongest mathematicians of the twentieth century. By contrast, non-self-adjoint CSL-algebras, particularly reflexive algebras, are only begins to be studied by W. B. Wrveson [1] 1974.

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ISOMORPHISMS OF CERTAIN TRIDIAGONAL ALGEBRAS

  • Choi, Taeg-Young;Kim, Si-Ju
    • The Pure and Applied Mathematics
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    • v.7 no.1
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    • pp.49-60
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    • 2000
  • We will characterize isomorphisms from the adjoint of a certain tridiag-onal algebra $AlgL_{2n}$ onto $AlgL_{2n}$. In this paper the following are proved: A map $\Phi{\;}:{\;}(AlgL_{2n})^{*}{\;}{\longrightarrow}{\;}AlgL_{2n}$ is an isomorphism if and only if there exists an operator S in $AlgL_{2n}$ with all diagonal entries are 1 and an invertible backward diagonal operator B such that ${\Phi}(A){\;}={\;}SBAB^{-1}S^{-1}$.

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LIE IDEALS IN TRIDIAGONAL ALGEBRA ALG𝓛

  • Kang, Joo Ho
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.351-361
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    • 2015
  • We give examples of Lie ideals in a tridiagonal algebra $Alg\mathcal{L}_{\infty}$ and study some properties of Lie ideals in $Alg\mathcal{L}_{\infty}$. We also investigate relationships between Lie ideals in $Alg\mathcal{L}_{\infty}$. Let k be a fixed natural number. Let $\mathcal{A}$ be a linear manifold in $Alg\mathcal{L}_{\infty}$ such that $T_{(2k-1,2k)}=0$ for all $T{\in}\mathcal{A}$. Then $\mathcal{A}$ is a Lie ideal if and only if $T_{(2k-1,2k-1)}=T_{(2k,2k)}$ for all $T{\in}\mathcal{A}$.

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 FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

  • Kang, Joo-Ho;Jo, Young-Soo
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.423-430
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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 article, we obtained the following : Let X = ($x_{i\sigma(i)}$ and Y = ($y_{ij}$ be operators in B(H) such that $X_{i\sigma(i)}\neq\;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${\frac{\parallel{\sum^n}_{i=1}E_iYf_i\parallel}{\parallel{\sum^n}_{i=1}E_iXf_i\parallel}n\;\epsilon\;N,E_i\;\epsilon\;L and f_i\;\epsilon\;H}$ < $\infty$ and $x_{i,\sigma(i)}y_{i,\sigma(i)}$ is real for all i = 1,2, ....

IDEALS IN A TRIDIAGONAL ALGEBRA ALGL

  • LEE, SANG KI;KANG, JOO HO
    • Journal of applied mathematics & informatics
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    • v.34 no.3_4
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    • pp.257-267
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    • 2016
  • We find examples of Ideals in a tridiagonal algebra ALGL and study some properties of Ideals in ALGL. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL and let A2,{k} ⊂ A ⊂ {T ∈ ALGL | T(2k-1,2k) = 0}. Then A is an ideal of ALGL if and only if A = A2,{k} where A2,{k} = {T ∈ ALGL | T(2k-1,2k) = 0, T(2k-1,2k-1) = T(2k,2k) = 0}. Let B be a subalgebra of ALGL such that B2,{j} ⊂ B ⊂ {T ∈ ALGL | T(2j+1,2j) = 0}. Then B is an ideal of ALGL if and only if B = B2,{j}, where B2,{j} = {T ∈ ALGL | T(2j+1,2j) = 0, T(2j,2j) = T(2j+1,2j+1) = 0}.

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, ….