In the last few decades, the concept of Birkhoff–James orthogonality has been used in
several applications. In this survey article, the results known on the necessary and sufficient …

We completely characterize smoothness of bounded linear operators between infinite
dimensional real normed linear spaces, probably for the very first time, by applying the …

We study best approximations to compact operators between Banach spaces and Hilbert
spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As …

This paper deals with study of Birkhoff-James orthogonality of a linear operator to a
subspace of operators defined between arbitrary Banach spaces. In case the domain space …

Abstract We study approximate Birkhoff–James orthogonality of bounded linear operators
defined between normed linear spaces XX and YY As an application of the results obtained …

We study left symmetric bounded linear operators in the sense of Birkhoff–James
orthogonality defined between infinite dimensional Banach spaces. We prove that a …

We study the geometry of L (X) w, the space of all bounded linear operators on a Banach
space X, endowed with the numerical radius norm, whenever the numerical radius defines a …

Abstract We study Birkhoff–James orthogonality of compact (bounded) linear operators
between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in …

This monograph is intended to be a gentle guide to some of the latest developments taking
shape in the broad area of geometry of Banach spaces. In particular, it provides insights into …

We study k-smoothness of bounded linear operators defined between arbitrary Banach
spaces. As an application, we characterize k-smooth operators defined from ℓ 1 n to an …