Dilation to inflations of S(Φ)

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Let T be a completely nonunitary contraction with rank (1 - T*T) = 1 on an n-dimensional Hubert space. We prove that (I) if n = 2 and S is an operator which has norm 1, attains its norm and satisfies W(S)⊆ W(T), then S has T as a direct summand, and (2) if ≥ 3 and S is an operator such that Sk dilates to Tk⊕Tk⊕ ... simultaneously for k = 1, 2,..., n - l and W(S)∩∂W(T)≠ θ, then S has T as a direct summand. (Here W(·) denotes the numerical range). These results generalize the corresponding ones for T the n × n nilpotent Jordan block.

Original languageEnglish
Pages (from-to)109-123
Number of pages15
JournalLinear and Multilinear Algebra
Issue number2-3
StatePublished - 1998


  • Compression of the shift
  • Dilation
  • Inflation
  • Numerical range
  • Power dilation


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