, Volume 42, Issue 3, pp 246-254

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.

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