On Property- and Relative Chebyshev Centres in Banach Spaces

Daptari, Soumitra and Paul, Tanmoy (2022) On Property- and Relative Chebyshev Centres in Banach Spaces. Taylor and Francis Ltd..

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Abstract

We demonstrate that if J is an M-ideal in a Lindenstrauss space X, then X satisfies the famous Smith and Ward identity, that is, (Formula presented.) for finite subsets F of X. We introduce strong property- (Formula presented.) for a triplet (Formula presented.) where X is a Banach space, V is a closed convex subset of X, and (Formula presented.) is a subfamily of closed, bounded subsets of X. We show that for a subspace V, the restricted Chebyshev centre for (Formula presented.) with respect to the unit ball of V is non-empty if the triplet (Formula presented.) has the strong property- (Formula presented.) We demonstrate that for an M-ideal J in a Lindenstrauss space X, the triplet (Formula presented.) has the strong property- (Formula presented.) where (Formula presented.) is the family of compact subsets of X. Some characterizations of the strong property- (Formula presented.) are given. Similar to the strong (Formula presented.) -ball property, we show that for a subspace V of X, a triplet (Formula presented.) has the strong property- (Formula presented.) if and only if (Formula presented.) has the property- (Formula presented.) and the set of restricted Chebyshev centres with respect to the unit ball of V is non-empty for (Formula presented.). © 2022 Taylor & Francis Group, LLC.

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IITH Creators:

IITH Creators	ORCiD

Item Type:

Other

Additional Information:

The second author’s research was supported by the SERB, India. Award No. MTR/2017/000061. The authors would like to express their gratitude to the referees for their thorough evaluation of the manuscript, which improved its readability and interpretation.

Uncontrolled Keywords:

-ball property; Chebyshev centre; Lindenstrauss space; M-ideal; property-; restricted Chebyshev centre

Subjects:

Mathematics

Divisions:

Department of Mathematics

Depositing User:

. LibTrainee 2021

Date Deposited:

25 Jul 2022 11:34

Last Modified:

25 Jul 2022 11:34