We observe that the classical notion of numerical radius gives rise to a notion of smoothness
in the space of bounded linear operators on certain Banach spaces, whenever the …

We completely characterize the left-symmetric points, the right-symmetric points, and the
symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete …

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 …

Abstract We study the Davis-Wielandt shell and the Davis-Wielandt radius of an operator on
a normed linear space X. We show that after a suitable modification, the modified Davis …

We introduce the notion of approximate smoothness in a normed linear space. We
characterize this property and show the connections between smoothness and approximate …

We explore the k-smoothness of bounded linear operators between Banach spaces, using
the newly introduced notion of index of smoothness. The characterization of the k …

We investigate the local preservation of Birkhoff-James orthogonality at a point by a linear
operator on a finite-dimensional Banach space and illustrate its importance in …

Generalizing the notion of numerical range and numerical radius of an operator on a
Banach space, we introduce the notion of joint numerical range and joint numerical radius of …

We show that the numerical index of any operator ideal is less than or equal to the minimum
of the numerical indices of the domain space and the range space. Further, we show that the …

We compute the numerical index of the two-dimensional real L p space for 6 5⩽ p⩽ 1+ α 0
and α 1⩽ p⩽ 6, where α 0 is the root of f (x)= 1+ x− 2−(x− 1 x+ x 1 x) and 1 1+ α 0+ 1 α 1= 1 …