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arXiv · 1907.01955

Smoothness and norm attainment of bounded bilinear operators between Banach spaces

Debmalya Sain
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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.

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Debmalya Sain. 2019-07-03. Smoothness and norm attainment of bounded bilinear operators between Banach spaces. https://arxiv.org/abs/1907.01955

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