ISOMORPHISMS OF CERTAIN TRIDIAGONAL ALGEBRAS

Choi, Taeg-Young; Choi, Taeg-Young; Kim, Si-Ju; Kim, Si-Ju

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P-ISSN3059-0604
E-ISSN3059-1309
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Vol.7 No.1

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Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309

2000, v.7 no.1, pp.49-60

Choi, Taeg-Young
Kim, Si-Ju

Choi,, T. , & Kim,, S. (2000). , 7(1), 49-60.

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Abstract

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 ${\Phi}(A){\;}={\;}SBAB^{-1}S^{-1}$.

keywords: tridiagonal algebra, isomorphism, spatially implemented

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Article Contents

Vol.7 No.1

Abstract

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics