Sain, D and Ray, A and Dey, S and Paul, K (2022) Some remarks on orthogonality of bounded linear operators-II. In: Acta Scientiarum Mathematicarum, 88 (3-4). pp. 807-820.
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Let X, Y be normed linear spaces. We continue exploring the validity of the Bhatia–Šemrl (BŠ) Property: “An operator T∈ L(X, Y) satisfies Bhatia–Šemrl Property if for any A∈ L(X, Y) , T⊥BA implies that there exists a unit vector x∈ X such that ‖ Tx‖ = ‖ T‖ and Tx⊥BAx.” A pair of normed linear spaces X, Y is said to be a BŠ pair if for every T∈ L(X, Y) , T satisfies the BŠ Property if and only if MT= D∪ (- D) , where D is a non-empty connected subset of SX. We show that ℓ1n,Y is a BŠ pair for any normed linear space Y, and also obtain some other results in this context. In particular, using the notion of norm attainment set,we characterize the space ℓ∞3 among all 3-dimensional polyhedral Banach spaces whose unit ball have exactly eight extreme points.
| Item Type: | Journal Article |
|---|---|
| Publication: | Acta Scientiarum Mathematicarum |
| Publisher: | Springer Nature |
| Additional Information: | The copyright for this article belongs to Springer Nature. |
| Keywords: | 46B20; 47L05; Birkhoff–James orthogonality; linear operators; norm attainment; polyhedral Banach spaces |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 21 Feb 2023 05:12 |
| Last Modified: | 21 Feb 2023 05:12 |
| URI: | https://eprints.iisc.ac.in/id/eprint/80572 |
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