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Unconditionally $p$-null sequences and unconditionally $p$-compact operators

Volume 224 / 2014

Ju Myung Kim 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.

Authors

  • Ju Myung KimDepartment of Mathematical Sciences
    Seoul National University
    Seoul, 151-747, Korea
    e-mail

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