Positive p-summing operators, vector measures and tensor products

Author:

Blasco Oscar

Abstract

In this paper we shall introduce a certain class of operators from a Banach lattice X into a Banach space B (see Definition 1) which is closely related to p-absolutely summing operators defined by Pietsch [8].These operators, called positive p-summing, have already been considered in [9] in the case p = 1 (there they are called cone absolutely summing, c.a.s.) and in [1] by the author who found this space to be the space of boundary values of harmonic B-valued functions in .Here we shall use these spaces and the space of majorizing operators to characterize the space of bounded p-variation measures and to endow the tensor product with a norm in order to get as its completion in this norm.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Positive multiple summing multilinear operators on bmL^p-spaces;SCIENTIA SINICA Mathematica;2023-05-01

2. $p$-variations of vector measures with respect to vector measures and integral representation of operators;Banach Journal of Mathematical Analysis;2015

3. Positive Multiple Summing and Concave Multilinear Operators on Banach Lattices;Mediterranean Journal of Mathematics;2014-01-29

4. p-VARIATION OF VECTOR MEASURES WITH RESPECT TO BILINEAR MAPS;Bulletin of the Australian Mathematical Society;2008-12

5. Maurey–Rosenthal factorization of positive operators and convexity;Journal of Mathematical Analysis and Applications;2004-09

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