Science in China Series A: Mathematics

, Volume 42, Issue 3, pp 246–254 | Cite as

Renorms and topological linear contractions on Hilbert spaces

  • Shih Mauhsiang
  • Tam Pingkwan
  • Tan Kok-Keong
Article

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.

Keywords

topological proper contraction topological strict contraction topological contraction simultaneous contractification Hilbert norm 

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Copyright information

© Science in China Press 1999

Authors and Affiliations

  • Shih Mauhsiang
    • 1
  • Tam Pingkwan
    • 2
  • Tan Kok-Keong
    • 3
  1. 1.Department of MathematicsChung Yuan UniversityChung-LiTaiwan 32023 China
  2. 2.Department of MathematicsChinese University of Hong KongHong KongChina
  3. 3.Department of Mathematics, Statistics, and Computing ScienceDalhousie UniversityHalifaxCanada

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