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 ...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.展开更多
基金Project supported by the Chinese University of Hong Kong (Grant No. 2060144)NSERC of Canada (Grant No. A8096)
文摘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.