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Properties of restrictions of the operator of multiplication by a continuous function

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Abstract

For the operatorA of multiplication by a continuous functiona (t) in the Hilbert spaceL 2[0, b]=H, we give a description of two sets of infinite-dimensional subspaces with infinite codimensions:I(A)={N⊂H:A/N is an isomorphism},K(A)={M⊂H: A/M is a compact mapping}. As an application, we consider the problem of determining whether the sequence {a(t)en(t)}, where {en(t)} is an orthonormal basis in L2[0,b], is an unconditional basis.

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References

  1. I. C. Gokhberg, A. S. Markus, and I. A. Fel'dman, “Normally solvable operators and ideals associated with them,”Izv. Mold. Fil. Akad. Nauk SSSR,10 (76), 51–59 (1960).

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Authors and Affiliations

  1. Zaporozhye University, Zaporozhye

    V. V. Shevchik

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  1. V. V. Shevchik
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1720–1722, December, 1995.

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Shevchik, V.V. Properties of restrictions of the operator of multiplication by a continuous function. Ukr Math J 47, 1968–1970 (1995). https://doi.org/10.1007/BF01060974

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  • DOI: https://doi.org/10.1007/BF01060974

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