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On the commutant of a multiplication operator and conditions of invertibility of its elements

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Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain a description of isomorphisms acting in the space of square summable functions and commuting with the operator of multiplication by a continuous piecewise monotone function. Preliminary corrections are made of some mistakes found in the statements of the paper [3].

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References

  1. P. Halmos,Hilbert Space in Problems [Russian translation], Mir, Moscow (1970).

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  2. M. A. Naimark,Normed Rings [in Russian], Gostekhteoretizdat, Moscow (1956).

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  3. A. H. Nasr, “The commutant of a multiplication operator,”J. Math. Phys.,23, No. 13, 2268–2270 (1982).

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  4. N. I. Berezovskii and S. S. Linchuk,Description of lnvertible Elements of the Commutant of Multiplication Operator in the Space of Square Summable Functions [in Russian], Deposited in Ukrain. Inst. of Sci. and Technol. Information No. 207-Yk 91, Chernovtsy (1991).

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Authors and Affiliations

  1. Chernovtsy University, Chernovtsy

    N. I. Berezovskii & S. S. Linchuk

Authors
  1. N. I. Berezovskii
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  2. S. S. Linchuk
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 21–25, January, 1993.

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Berezovskii, N.I., Linchuk, S.S. On the commutant of a multiplication operator and conditions of invertibility of its elements. Ukr Math J 45, 21–25 (1993). https://doi.org/10.1007/BF01062033

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  • DOI: https://doi.org/10.1007/BF01062033

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