An overview of semi-continuity results on the spectral radius and positivity |
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| Authors: | Guy Degla |
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| Institution: | Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Institute of Mathematics, No. 55 Zhong Guan Cun East Road, Beijing, China |
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| Abstract: | Our aim is to provide a novelly comprehensive and unifying approach to showing the continuous dependence of the spectral radius of compact linear operators defined on Banach spaces (with specific attention to positive operators defined on normal Banach spaces) and emphasizing that the upper semi-continuity generally holds unlike the lower semi-continuity. |
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| Keywords: | Spectral radius Semi-continuity Compactness Positivity Weighted shift operator |
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