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A symmetric operator and its Kaufman's representation

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Abstract

Kaufman’s representation theorem is that a closed operator S with a dense domain in Hilbert space H is represented by a quotient S = B/(1 − B * B)1/2 for a unique contraction B. When S is a symmetric operator, what is a condition of the spectrum of B to admit selfadjoint extensions of S? In this note, it is shown that if there are no negative real points in the spectrum of B, then S has selfadjoint extensions.

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Authors and Affiliations

  1. Hasuda 518-4-301, Hasuda Saitama, 349-0115, Japan

    G. Hirasawa

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  1. G. Hirasawa
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Hirasawa, G. A symmetric operator and its Kaufman's representation. Periodica Mathematica Hungarica 49, 43–47 (2004). https://doi.org/10.1023/B:MAHU.0000040538.77157.56

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  • DOI: https://doi.org/10.1023/B:MAHU.0000040538.77157.56

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