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Characterizations of Banach spaces which are not isomorphic to any of their proper subspaces

In: Mathematica Slovaca, vol. 65, no. 1
Qingping Zeng - Huaijie Zhong

Details:

Year, pages: 2015, 169 - 178
Keywords:
Banach spaces, left multiplication operators, Drazin spectrum, left Drazin spectrum
About article:
In this note we obtain some characterizations of Banach spaces which are not isomorphic to any of their proper subspaces. In particular, we show that a Banach space $X$ is not isomorphic to any of its proper subspaces if and only the equality $σRD(LT)=σLD(T)$ holds for every bounded linear operator $T$ on $X$ if and only if $int(σ(T)) \subseteqσLD(T)$ holds for every bounded linear operator $T$ on $X$, where $LT$ denotes the left multiplication operator by $T$.
How to cite:
ISO 690:
Zeng, Q., Zhong, H. 2015. Characterizations of Banach spaces which are not isomorphic to any of their proper subspaces. In Mathematica Slovaca, vol. 65, no.1, pp. 169-178. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0014

APA:
Zeng, Q., Zhong, H. (2015). Characterizations of Banach spaces which are not isomorphic to any of their proper subspaces. Mathematica Slovaca, 65(1), 169-178. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0014
About edition: