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Contractions with a unilateral shift summand are reflexive

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Abstract

If T is a contraction on the Hilbert space H and there is an invariant subspace K for T such that T/K is similar to a backward shift, then T is reflexive. If “similarity” is replaced by “quasi-similarity”, then the same conclusion holds under the additional condition that the defect index of T be finite.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan Republic of China

    Pei Yuan Wu

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  1. Pei Yuan Wu
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This research was partially supported by National Science Council (Republic of China).

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Wu, P.Y. Contractions with a unilateral shift summand are reflexive. Integr equ oper theory 7, 899–904 (1984). https://doi.org/10.1007/BF01195874

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  • DOI: https://doi.org/10.1007/BF01195874

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