Science in China Series A: Mathematics

, Volume 42, Issue 3, pp 246-254

First online:

Renorms and topological linear contractions on Hilbert spaces

  • Shih MauhsiangAffiliated withDepartment of Mathematics, Chung Yuan University
  • , Tam PingkwanAffiliated withDepartment of Mathematics, Chinese University of Hong Kong
  • , Tan Kok-KeongAffiliated withDepartment of Mathematics, Statistics, and Computing Science, Dalhousie University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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 contraction topological strict contraction topological contraction simultaneous contractification Hilbert norm