Lifting some approximation properties from a dual space to the Banach space X
Tom 257 / 2021
Studia Mathematica 257 (2021), 287-294
MSC: Primary 46B28, 47L20; Secondary 46B45.
DOI: 10.4064/sm190826-20-2
Opublikowany online: 5 October 2020
Streszczenie
For a fixed Banach operator ideal \mathcal A , we characterize \mathcal A -compact sets (in the sense of Carl and Stephani) that are determined by c_0 via the Banach composition ideal \mathcal A \circ \mathfrak K_{\infty }, with \mathfrak K_{\infty } the Banach ideal of Fourie and Swart. This characterization allows us to relate \mathcal K _{\mathcal A} -approximation properties on a Banach space and \mathcal K _{\mathcal B} -approximation properties on its dual space, where \mathcal A and \mathcal B are ideals linked by some classical procedures. These approximation properties have been widely studied in several papers in the last years.
