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Papers by Pradipta Bandyopadhyay

Archiv der Mathematik, 2021

In this short note, we answer two questions about Gurariy spaces asked in the literature in the a... more In this short note, we answer two questions about Gurariy spaces asked in the literature in the affirmative. We also prove the analogue of one of the results for the noncommutative Guariy space.

K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if an... more K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.

Abstract. A subspace Y of a Banach space X is an almost constrained (AC) subspace if any family o... more Abstract. A subspace Y of a Banach space X is an almost constrained (AC) subspace if any family of closed balls centred at points of Y that intersects in X also intersects in Y. In this paper, we show that a subspace H of finite codimension in C(K), the space of continuous functions on a compact Hausdorff space K, is an AC-subspace if and only if H is the range of a norm one projection in C(K). We also give a simple proof that the implication “AC ⇒ 1-complemented ” holds for any subspace of c0(Γ) and c. 1.

The man in the making Prasanta Chandra Mahalanobis was one of the last generation of men and wome... more The man in the making Prasanta Chandra Mahalanobis was one of the last generation of men and women whose life and times were Iargely shaped by the traditions of the Bengal Renaissance .

Journal of Mathematical Analysis and Applications

We work with real Banach spaces. We will denote by B(X), S(X) and B[x, r] respectively the closed... more We work with real Banach spaces. We will denote by B(X), S(X) and B[x, r] respectively the closed unit ball, the unit sphere and the closed ball of radius r > 0 around x ∈ X. We will identify any element x ∈ X with its canonical image in X∗∗. All subspaces we usually consider are norm closed. Definition 1.1. (a) We say A ⊆ B(X∗) is a norming set for X if ‖x‖ = sup{x∗(x) : x∗ ∈ A}, for all x ∈ X. A closed subspace F ⊆ X∗ is a norming subspace if B(F ) is a norming set for X. (b) A Banach space X is (i) nicely smooth if X∗ contains no proper norming subspace; (ii) has the Ball Generated Property (BGP) if every closed bounded convex set in X is ball-generated, i.e., intersection of finite union of balls; (iii) has Property (II) if every closed bounded convex set in X is the intersection of closed convex hulls of finite union of balls, or equivalently, w*-points of continuity (w*-PCs) of B(X∗) are norm dense in S(X∗) [5]; (iv) has the Mazur Intersection Property (MIP) (or, Property (...

Illinois Journal of Mathematics

We study the abstract geometric notion of unitaries in a Banach space characterized in terms of t... more We study the abstract geometric notion of unitaries in a Banach space characterized in terms of the equivalence of the norm determined by the state space.

Taiwanese Journal of Mathematics

Journal of Convex Analysis, 2006

Extracta Mathematicae, 2007

K.\ S.\ Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if ... more K.\ S.\ Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result

In this work, we obtain some necessary and some sufficient conditions for a space to be nicely sm... more In this work, we obtain some necessary and some sufficient conditions for a space to be nicely smooth, and show that they are equivalent for separable or Asplund spaces. We obtain a sufficient condition for the Ball Generated Property (BGP), and conclude that Property (II)(II)(II) implies the BGP, which, in turn, implies the space is nicely smooth. We show that

Contemporary Mathematics, 2003

Veselý has studied Banach spaces that admit weighted Chebyshev centres for finite sets. Subsequen... more Veselý has studied Banach spaces that admit weighted Chebyshev centres for finite sets. Subsequently, Bandyopadhyay and Rao had shown, inter alia, that L 1-preduals have this property. In this work, we investigate why and to what extent are these results true and thereby explore when a more general family of sets admit weighted Chebyshev centres. We extend and improve upon some earlier results in this general setup and relate them with a modified notion of minimal points. Special cases when we consider the family of all finite, or more interestingly, compact subsets lead to characterizations of L 1-preduals. We also consider some stability results.

Lecture Notes in Mathematics, 1992

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