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題 名 | Boundedness Stability Properties of Linear and Affine Operators |
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作 者 | 陳國強; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 2:1 1998.03[民87.03] |
頁 次 | 頁111-125 |
分類號 | 315 |
關鍵詞 | Affine operator; Jordan cell; Spectrum; Jordan canonical form; Complexification; Block decomposition; Functionally bounded; Riesz decomposition; Compact operator; Perturbation; Strict contraction; Quasinilpotent operator; Riesz operator; Normal operator; Unitarily equivalent; Subnormal operator; |
語 文 | 英文(English) |
英文摘要 | Let E be a vector space in which some notion of boundedness is defined. Then T: E → E is said to have the boundedness stability property (BSP) if for each x �e E, the sequence (T □ ) □ is bounded whenever a subsequence (T ���[ x) □ is bounded. It is shown that (1) every affine operator on a finite-dimensional Banach space has the (BSP); (2) every affine operator on an infinite-dimensional vector space has the functional (BSP); (3) when E is an infinite-dimensional Banach space, an affine operator T on E has the (BSP) if its linear part AT = T - T(0) is a compact perturbation of a bounded linear operator with spectral radius less than one and (4) when E is a Hilbert space, every normal or subnormal bounded linear operator has the (BSP). Some results on affine operators on a Hilbert space whose linear parts are normal or subnormal are also obtained. Finally, some problems are posed. |
本系統中英文摘要資訊取自各篇刊載內容。