Self-Adjoint Interpolation on AX=Y in a Tridiagonal Algebra Algmathcal L

Given operators X and Y acting on a separable Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate self-adjoint interpo-lation problems for operators in a tridiagonal algebra: Let L be a subspace lattice acting on a separable complex Hi...

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Bibliographic Details
Published inHonam mathematical journal Vol. 36; no. 1; pp. 29 - 32
Main Authors Joo Ho Kang, Sangki Lee
Format Journal Article
LanguageKorean
Published 호남수학회 30.03.2014
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Summary:Given operators X and Y acting on a separable Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate self-adjoint interpo-lation problems for operators in a tridiagonal algebra: Let L be a subspace lattice acting on a separable complex Hilbert space H and let X = (χij) and Y = (yij) be operators acting on H. Then the following are equivalent: (1)There exists a self-adjoint operator A = (aij) in AlgL such that AX = Y. (2) There is a bounded real sequence {αn} such that yij = αiχij for i,j ∈ N.
Bibliography:THE HONAM MATHEMATICAL SOCIETY KWANGJU
ISSN:1225-293X