Norm equalities of analytic mappings into Hilbert spaces |
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| Authors: | Dr. J. Globevnik |
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| Affiliation: | 1. Department of Mathematics, University of Kentucky, 40506, Lexington, KY, USA
2. Institute of Mathematics, University of Ljubljana, 61000, Ljubljana, Yugoslavia
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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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