Vector-valued Lorentz sequence spaces and their dual spaces
Volume 166 / 2021
Colloquium Mathematicum 166 (2021), 53-73
MSC: Primary 46A45; Secondary 46B10.
DOI: 10.4064/cm8005-8-2020
Published online: 11 February 2021
Abstract
We introduce and investigate the Banach space of vector-valued strongly Lorentz sequences. We prove that this space is a topological dual of a class of weakly Lorentz sequences; moreover, we prove that also the class of weakly Lorentz sequences is a topological dual of a class of strongly Lorentz sequences. We apply these results to obtain a characterization of the bidual of Lorentz summing linear operators.
