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- W2900086025 abstract "Given a Banach space E,we askwhich closed subspacesmay be realised as the kernel of a bounded operator E → E.We prove some positive results which imply in particular that when E is separable every closed subspace is a kernel. Moreover, we show that there exists a reflexive Banach space E which contains a closed subspace that cannot be realised as the kernel of any bounded operator on E. This implies that the Banach algebraB(E) of bounded operators on E fails to be weak*-topologically left Noetherian in the sense of [7]. The Banach space E that we use is the dual of one of Wark’s non-separable, reflexive Banach spaces with few operators." @default.
- W2900086025 created "2018-11-16" @default.
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- W2900086025 date "2020-08-24" @default.
- W2900086025 modified "2023-09-23" @default.
- W2900086025 title "Subspaces that can and cannot be the kernel of a bounded operator on a Banach space" @default.
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- W2900086025 doi "https://doi.org/10.1515/9783110602418-011" @default.
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