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Renorms and topological linear contractions on Hilbert spaces

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Abstract

Properties of and the relationships between (topological) proper contractions, (topological) strict contractions and (topological) contractions are investigated. Explicit renorms are constructed so that all operators in a (finite or countable) family or a semigroup simultaneously become proper contractions or strict contractions. Some results are obtained for operator weighted shifts or operator weighted continuous shifts to be topological strict contractions.

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Authors and Affiliations

  1. Department of Mathematics, Chung Yuan University, Chung-Li, Taiwan 32023 China

    Shih Mauhsiang

  2. Department of Mathematics, Chinese University of Hong Kong, Hong Kong, China

    Tam Pingkwan

  3. Department of Mathematics, Statistics, and Computing Science, Dalhousie University, B3H 3J5, Halifax, Nova Scotia, Canada

    Tan Kok-Keong

Authors
  1. Shih Mauhsiang
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  2. Tam Pingkwan
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  3. Tan Kok-Keong
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Additional information

Project supported by the Chinese University of Hong Kong (Grant No. 2060144) and NSERC of Canada (Grant No. A8096).

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Mauhsiang, S., Pingkwan, T. & Kok-Keong, T. Renorms and topological linear contractions on Hilbert spaces. Sci. China Ser. A-Math. 42, 246–254 (1999). https://doi.org/10.1007/BF02879058

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  • DOI: https://doi.org/10.1007/BF02879058

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