Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators

Arpita Mal, Kallol Paul, T. S. S. R. K. Rao, Debmalya Sain

Published 2018-11-07Version 1

We study approximate Birkhoff-James orthogonality of bounded linear operators defined between normed linear spaces $\mathbb{X}$ and $\mathbb{Y}.$ As an application of the results obtained, we characterize smoothness of a bounded linear operator $T$ under the condition that $\mathbb{K}(\mathbb{X},\mathbb{Y}),$ the space of compact linear operators is an $M-$ideal in $\mathbb{L}(\mathbb{X},\mathbb{Y}),$ the space of bounded linear operators.