Renorms and topological linear contractions on Hilbert spaces
- 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.