Debmalya Sain

TL;DR: In this paper, it was shown that T ∈ L ( l p 2 ) (p ≥ 2, p ≠ ∞ ) is left symmetric with respect to Birkhoff-James orthogonality if and only if T is the zero operator.

TL;DR: In this paper, it was shown that a finite dimensional real normed linear space X is an inner product space iff for any linear operator T on X, T attains its norm at e 1, e 2 ∈ S X implies that T has norm at span { e 1, e 2 } ∩ S X.

TL;DR: In this paper, a sufficient condition for smoothness of bounded linear operators on Banach spaces was presented, where T is a smooth point in B (X, Y ) if T attains its norm at unique (upto multiplication by scalar) vector x ∈ S X, Tx is a smoothing point of Y and sup y ∈ C ‖ T y ‖ ‖, T ‖ for all closed subsets C of S X with d ( ± x, C ) > 0.

TL;DR: In this paper, the authors explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment, and obtain a characterization of smooth Banach spaces in terms of smooth norm attainment and Birkhoff-James orthogonality.

TL;DR: In this paper, a complete characterization of the Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces is given, provided the dual space is strictly convex.