, Volume 42, Issue 3, pp 246-254

Renorms and topological linear contractions on Hilbert spaces

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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.