Lifting some approximation properties from a dual space $X’$ to the Banach space $X$

TURCO, PABLO; KIM, JU MYUNG; LASSALLE, SILVIA

STUDIA MATHEMATICA

POLISH ACAD SCIENCES INST MATHEMATICS

Lugar: VARSOVIA; Año: 2020

0039-3223

Fixed a Banach operator ideal $A$, we characterize $A$-compact sets (in the sense of Carl and Stephani) that are determined by $c_0$ via the Banach composition ideal $Acirc mathfrak K_{infty}$, with $mathfrak K_{infty}$ the Banach ideal of Fourie and Swart. This characterization allows us to relate $K_A$-approximation properties on a Banach space and $K_B$-approximation properties on its dual space, where $A$ and $B$ are ideals linked by some classical procedures. These approximation properties have been widely studied in several papers in the last years.