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??? |
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頁(從 - 到) | 109-123 |
頁數 | 15 |
期刊 | Linear and Multilinear Algebra |
卷 | 45 |
發行號 | 2-3 |
DOIs | |
出版狀態 | 已出版 - 1998 |