Dilation to inflations of S(Φ)

Hwa Long Gau, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

16 引文 斯高帕斯(Scopus)

摘要

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.

原文???core.languages.en_GB???
頁(從 - 到)109-123
頁數15
期刊Linear and Multilinear Algebra
45
發行號2-3
DOIs
出版狀態已出版 - 1998

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