Uniform factorization for p-compact sets of p-compact linear operators - Caliskan, Erhan; Keten, Aysegul (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016)
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.
Keywords: Banach spaces; p-Compact sets; p-Compact linear operators; Factorization; Tensor product; Homogeneous polynomials; FINITE-RANK OPERATORS; APPROXIMATION PROPERTY; SUBSPACES; ADJOINTS; MAPPINGS; SPACES; IDEAL; L(P); Mathematics