Uniform factorization for p-compact sets of p-compact linear operators


Caliskan E., Keten A.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.437, no.2, pp.1058-1069, 2016 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 437 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1016/j.jmaa.2016.01.030
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1058-1069

Abstract

Obtaining a factorization of p-compact linear operators via universal Banach spaces, and using the lifting property of quotient maps for p-compact sets we prove a factorization result for relatively r-compact subsets of p-compact operators, where r >= 2, 1 <= p <= r < infinity. To apply our results to homogeneous polynomials, in particular, we show that relatively p-compact subsets of a Banach space of p-compact operators are collectively p-compact. (C) 2016 Elsevier Inc. All rights reserved.