This is an announcement for the paper “Approximate Birkhoff-James orthogonality and smoothness in the space of bounded linear operators” by Arpita Malhttps://arxiv.org/search/math?searchtype=author&query=Mal%2C+A, Kallol Paulhttps://arxiv.org/search/math?searchtype=author&query=Paul%2C+K, T.S.S.R.K. Raohttps://arxiv.org/search/math?searchtype=author&query=Rao%2C+T+S+S+R+K, Debmalya Sainhttps://arxiv.org/search/math?searchtype=author&query=Sain%2C+D.

Abstract: 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.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1811.02772