Short five lemmas in Banach spaces
Consider a commutative diagram of bounded linear operators between Banach spaces\[ \begin{CD}\qquad\qquad\qquad\qquad 0 @>>> X @>{J}>> Y @>{Q}>> Z @>>> 0\\ @. @V{A}VV @V{B}VV @V{C}VV @. \qquad\qquad\qquad \qquad \\\qquad\qquad\qquad\qquad 0 @>>> X @>&g...
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| Veröffentlicht in: | Electronic Journal of Linear Algebra 2014-11, Vol.27 (1) |
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| container_title | Electronic Journal of Linear Algebra |
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| creator | Zeng, Qingping Zhong, Huaijie |
| description | Consider a commutative diagram of bounded linear operators between Banach spaces\[ \begin{CD}\qquad\qquad\qquad\qquad 0 @>>> X @>{J}>> Y @>{Q}>> Z @>>> 0\\ @. @V{A}VV @V{B}VV @V{C}VV @. \qquad\qquad\qquad \qquad \\\qquad\qquad\qquad\qquad 0 @>>> X @>>{J}> Y @>>{Q}> Z @>>> 0\end{CD} \]with exact rows.In what ways are the spectral and local spectral properties of $B$ related to those of the pairs of operators $A$ and $C$?In this paper, we give our answers to this general question using tools from local spectral theory. |
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| title | Short five lemmas in Banach spaces |
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