Smoothness and norm attainment of bounded bilinear operators between Banach spaces
Functional Analysis
2019-07-04 v1
Abstract
We study the smoothness and the norm attainment of bounded bilinear operators between Banach spaces, using the concepts of Birkhoff-James orthogonality and semi-inner-products. In the finite-dimensional case, we characterize Birkhoff-James orthogonality of bilinear operators in terms of the norm attainment set. This yields a nice characterization of smoothness of bilinear operators between Banach spaces, in the finite-dimensional case. Without any restriction on the dimension of the space, we obtain a complete characterization of the norm attainment set of a bounded bilinear operator using semi-inner-products, which is particularly useful when the concerned Banach spaces are smooth.
Keywords
Cite
@article{arxiv.1907.01955,
title = {Smoothness and norm attainment of bounded bilinear operators between Banach spaces},
author = {Debmalya Sain},
journal= {arXiv preprint arXiv:1907.01955},
year = {2019}
}