Science in China Series A: Mathematics

, Volume 42, Issue 3, pp 246–254

Renorms and topological linear contractions on Hilbert spaces


  • Shih Mauhsiang
    • Department of MathematicsChung Yuan University
  • Tam Pingkwan
    • Department of MathematicsChinese University of Hong Kong
  • Tan Kok-Keong
    • Department of Mathematics, Statistics, and Computing ScienceDalhousie University

DOI: 10.1007/BF02879058

Cite this article as:
Mauhsiang, S., Pingkwan, T. & Kok-Keong, T. Sci. China Ser. A-Math. (1999) 42: 246. doi:10.1007/BF02879058


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.


topological proper contractiontopological strict contractiontopological contractionsimultaneous contractificationHilbert norm
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© Science in China Press 1999