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Information Journal Paper

Title

Reflexivity of Cowen-Douglas Operators

Pages

  83-88

Abstract

 For a connected open subset Ω of the plane and n a positive integer, let B_n (Ω ) be the Cowen-Douglas class of operators. In this article, for a special case of Ω , we show that if T∈ B_n (Ω ) and its canonical model is a Von Neumann operator, then T is reflexive. In the main theorem of this paper we assume that the adjoint of the canonical model associated with g. B. K is a Von Neuman operator. We may replace this by the assumption that ‖ M_P ‖ ≤ c‖ P‖ _Ω or ‖ M_P ‖ =c‖ P‖ _Ω for every polynomial P. Actually K is the reproducing kernel for a coanalytic functional Hilbert space K on which we can define the operator M_z^* of multiplication byz. Note that if K is stricly positive kernel function on Λ , it gives rise to a functional Hilbert space on Λ with reproducing kernel K. A bounded linear operator T is said to be Von Neumann if the C^*-algebra generated by T is a Von Neumann algebra. We must point out that the operators of Cowen-Douglas class is not reflexive in general, since every operator of this class is unitarily equivalent to the adjoint of non-reflexive operator multiplication by Z ̅ . We need to impose the additional conditions for reflexivity of T.

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    APA: Copy

    Elon Kashkooly, Ali, & FATAHI, ZAHRA. (2021). Reflexivity of Cowen-Douglas Operators. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 7(31 ), 83-88. SID. https://sid.ir/paper/954162/en

    Vancouver: Copy

    Elon Kashkooly Ali, FATAHI ZAHRA. Reflexivity of Cowen-Douglas Operators. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2021;7(31 ):83-88. Available from: https://sid.ir/paper/954162/en

    IEEE: Copy

    Ali Elon Kashkooly, and ZAHRA FATAHI, “Reflexivity of Cowen-Douglas Operators,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 7, no. 31 , pp. 83–88, 2021, [Online]. Available: https://sid.ir/paper/954162/en

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