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A functional calculus in hilbert space based on operator valued analytic functions

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Abstract

A homomorphic map is defined from the algebra of norm bounded analyticN-operator valued functions in the unit disc into the algebra of bounded operators in Hilbert spaces represented as left invariant subspaces ofH 2(N), and the spectral properties of the map are studied.

The subclass of functions having norm bound one in the disc is characterized in terms of the power series coefficients.

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Authors and Affiliations

  1. Department of Applied Mathematics, Tel Aviv University, Tel Aviv, Ramat Aviv, Israel

    Paul A. Fuhrmann

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  1. Paul A. Fuhrmann
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Additional information

This paper was partially supported by the National Science Foundation under contract NSF GP-5455.

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Fuhrmann, P.A. A functional calculus in hilbert space based on operator valued analytic functions. Israel J. Math. 6, 267–278 (1968). https://doi.org/10.1007/BF02760259

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  • DOI: https://doi.org/10.1007/BF02760259

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