Geometry of $\ell_p$-direct sums of normed linear spaces
Functional Analysis
2023-09-26 v1
Abstract
We consider -direct sums () and -direct sums of countably many normed spaces and find the duals of these spaces. We characterize the support functionals of arbitrary elements in these spaces to characterize smoothness and approximate smoothness, both locally and globally. These results let us obtain examples of spaces that are not approximately smooth but where every non-zero element is approximately smooth. We also characterize Birkhoff-James orthogonality and its pointwise symmetry in these spaces.
Keywords
Cite
@article{arxiv.2309.14252,
title = {Geometry of $\ell_p$-direct sums of normed linear spaces},
author = {Babhrubahan Bose},
journal= {arXiv preprint arXiv:2309.14252},
year = {2023}
}