Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

In this article, we prove the proximinality of closed unit ball of M-ideals of compact operators on Banach spaces. We show that every positive (self-adjoint) operator on a Hilbert space has a positive (self-adjoint) compact approximant from the closed unit ball of space of compact operators. We also show that K(L1), the space of compact operators on L1, is ball proximinal in B(L1), the space of bounded operators on L1, even though K(L1) is not an M-ideal in B(L1). Moreover, we prove the ball proximinality of M-embedded spaces in their biduals. © 2021 American Mathematical Society. All rights reserved.

Department of Mathematics

World University root node

Proceedings of the American Mathematical Society

Ball proximinality of m-ideals of compact operators

We analyse the structure of finite dimensional subspaces of the set of points of strong subdifferentiability in a dual space. In a dual L1(μ) space, such a subspace is in the discrete part of the Yoshida-Hewitt type decomposition. In this set up, any Banach space consisting of points of strong subdifferentiability is necessarily finite dimensional. Our results also lead to streamlined and new proofs of results from the study of strong proximinality for subspaces of finite co-dimension in a Banach space. © 2021 Heldermann Verlag.

Journal of Convex Analysis

Structure of sets of strong subdifferentiability in dual L1-spaces

In this article, we characterize finite co-dimensional strongly ball proximinal subspaces of L1-predual spaces and prove that they are precisely the finite co-dimensional strongly proximinal subspaces. © 2019 Heldermann Verlag. All rights reserved.

Characterization of strong ball proximinality in L1-predual spaces

In this article, we discuss the strong proximinality of the closed unit ball of closed linear subspaces of L1-predual spaces. We prove that M-ideals in L1-predual spaces are strongly ball proximinal. We characterize finite co-dimensional strongly ball proximinal closed linear subspaces of C(K) spaces and prove that they are precisely the finite co-dimensional strongly proximinal closed linear subspaces of C(K). For a Choquet simplex K, we give a sufficient condition for the strong ball proximinality of finite co-dimensional closed linear subspaces of A(K) spaces. We prove that metric projection onto a finite co-dimensional strongly proximinal closed linear subspace of an L1-predual space is Hausdorff metric continuous. Moreover, we prove that the metric projection onto the closed unit ball of an M-ideal in an L1-predual space is Hausdorff metric continuous. © 2016 Elsevier Inc.

Journal of Approximation Theory

Strong ball proximinality and continuity of metric projection in L1-predual spaces

In this paper, we study two optimization problems where solutions on a dense set yield global solution. We study these problems for spaces of Bochner integrable functions and for spaces of continuous functions. The first one deals with expressing the length of a vector as a sum of the distance to a best approximation and minimal best approximation and the second one relates to approximating a subsequence of a minimizing sequence with a sequence of proximinal vectors. © 2016 Belgian Mathematical Society. All rights reserved.

Bulletin of the Belgian Mathematical Society - Simon Stevin

Optimization through dense sets

We investigate a variation of the transitivity problem for proximinality properties of subspaces and intersection properties of balls in Banach spaces. For instance, we prove that if Z⊆Y⊆X, where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X, then Z is strongly proximinal in X. Towards this, we prove that a finite co-dimensional proximinal subspace Y of X is strongly proximinal in X if and only if Y⊥⊥ is strongly proximinal in X**. We also prove that in an abstract L1-space, the notions of strongly subdifferentiable points and quasi-polyhedral points coincide. We also give an example to show that M-ideals need not be ball proximinal. Moreover, we prove that in an L1-predual space, M-ideals are ball proximinal. © 2015 Elsevier Inc.

Journal of Mathematical Analysis and Applications

Strong proximinality and intersection properties of balls in Banach spaces

For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. We prove that if the strong 11/ 2-ball property is separably determined for Y in X, then L 1(μ, Y) has the strong 11/2ball property in L 1(μ, X). For an M-embedded space X, we give a class of elements in L 1(μ, X having best approximations from L 1(μ, X). We also prove that some of the proximinality properties are stable under polyhedral direct sums of Banach spaces. © 2014 Copyright Taylor &amp; Francis Group, LLC.

Numerical Functional Analysis and Optimization

Proximinality properties in Lp(μ, X) and polyhedral direct sums of banach spaces

We introduce a weaker notion of central subspace called almost central subspace, and we study Banach spaces that belong to the class (GC), introduced by Veselý (1997). In particular, we prove that if Y is an almost central subspace of a Banach space X such that Y is in the class (GC), then Y is a central subspace of X . We also prove that if Y is a semi M -ideal in a Banach space X such that Y is an almost central subspace of X, then Y is an M -ideal in X. Certain stability results for quotient spaces, injective tensor product spaces, and polyhedral direct sums of Banach spaces are also derived. © 2013 C. R. Jayanarayanan.