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Norm equalities of analytic mappings into Hilbert spaces

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Abstract

LetD be a subset of a complex linear spaceL such that for everyu∈D,v∈L the setΩ(u, v) = {ζ∣u+ζv∈D} is an open connected set in the complex plane. Denote byA (D, X) the linear space of allG-analytic mappings fromD to a complex Hilbert spaceX.Theorem: LetZ be a complex linear space and letA, B be linear operators fromZ toA (D, X), A (D, Y), respectively, whereX, Y are complex Hilbert spaces. If ∥(A p)u∥ X =∥(B p)u∥ Y (p∈Z,u∈D) then a maximal partial isometryW:X→Y exists such that(Bp)u=W((Ap)u) (p∈Z, u∈D).

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA

    J. Globevnik

  2. Institute of Mathematics, University of Ljubljana, 61000, Ljubljana, Yugoslavia

    J. Globevnik

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  1. J. Globevnik
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This work was supported by the Boris Kidrič Fund, Ljubljana, Yugoslavia.

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Globevnik, J. Norm equalities of analytic mappings into Hilbert spaces. Monatshefte für Mathematik 79, 299–301 (1975). https://doi.org/10.1007/BF01647330

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  • DOI: https://doi.org/10.1007/BF01647330

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