Uniqueness of Hahn–Banach extensions and some of its variants

Daptari, Soumitra and Paul, Tanmoy (2022) Uniqueness of Hahn–Banach extensions and some of its variants. Advances in Operator Theory, 7 (3). ISSN 2662-2009

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In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case in which Y is an ideal of X. In this context, we study the property (U)/(SU)/(HB) and property (wU)/(k-U) for a subspace Y of a Banach space X. We obtain various new characterizations of these properties. We study different kinds of stabilities resulting from these properties in the tensor product spaces, spaces of Bochner integrable functions, and the higher duals of Banach spaces. We discuss various examples in the classical Banach spaces, where the aforementioned properties are satisfied and where they fail. It is established that a hyperplane in c has property (HB) if and only if it is an M-summand. It is observed that a finite-dimensional subspace Y has property (k-U) in c, in addition to that if Y is an ideal, then Y∗ is a k-strictly convex subspace of ℓ1 for some natural k. © 2022, Tusi Mathematical Research Group (TMRG).

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IITH Creators:
IITH CreatorsORCiD
Paul, Tanmoyhttp://orcid.org/0000-0002-2043-3888
Item Type: Article
Additional Information: The research of the second author was supported by SERB (Science and Engineering Research Board), India, Award no. MTR/2017/000061.
Uncontrolled Keywords: k-Chebyshev subspace; L1-predual; M-ideal; Property (HB); Property (SU); Property (U); Property (wU)
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 18 Oct 2022 09:50
Last Modified: 18 Oct 2022 09:50
URI: http://raiith.iith.ac.in/id/eprint/11005
Publisher URL: http://doi.org/10.1007/s43036-022-00201-5
OA policy: https://v2.sherpa.ac.uk/id/publication/41437
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