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Cites:

1

Information Journal Paper

Title

OPERATOR-VALUED BASES ON HILBERT SPACES

Pages

  195-212

Abstract

 In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov -basis theory, using operator-algebraic methods. We prove several results for ov -basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov -basis are continuous. We also define the concepts of Bessel, Hilbert ov -basis and obtain some characterizations of them. We study orthonormal and Riesz ov -bases for Hilbert spaces. Finally we consider the stability of ov -bases under small perturbations. We generalize a result of Paley-Wiener [4] to the situation of ov -basis.

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    APA: Copy

    ASGARI, M.S.. (2013). OPERATOR-VALUED BASES ON HILBERT SPACES. JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA, 2(4), 195-212. SID. https://sid.ir/paper/335587/en

    Vancouver: Copy

    ASGARI M.S.. OPERATOR-VALUED BASES ON HILBERT SPACES. JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA[Internet]. 2013;2(4):195-212. Available from: https://sid.ir/paper/335587/en

    IEEE: Copy

    M.S. ASGARI, “OPERATOR-VALUED BASES ON HILBERT SPACES,” JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA, vol. 2, no. 4, pp. 195–212, 2013, [Online]. Available: https://sid.ir/paper/335587/en

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