Unconditionally $p$-null sequences and unconditionally $p$-compact operators
Volume 224 / 2014
Studia Mathematica 224 (2014), 133-142
MSC: 46B45, 46B50, 46B28, 47L20.
DOI: 10.4064/sm224-2-2
Abstract
We investigate sequences and operators via the unconditionally $p$-summable sequences. We characterize the unconditionally $p$-null sequences in terms of a certain tensor product and then prove that, for every $1 \leq p < \infty $, a subset of a Banach space is relatively unconditionally $p$-compact if and only if it is contained in the closed convex hull of an unconditionally $p$-null sequence.
