Download this article
 Download this article For screen
For printing
Recent Issues
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
Statement, 2023
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author index
To appear
Other MSP Journals
On summability of nonlinear operators

Daniel Pellegrino and Joedson Santos

Vol. 6 (2024), No. 1, 115–135

The main motivation of this paper is the following general problem: under what (nontrivial) conditions a vector-valued m-linear operator T : p × × p q satisfies a summability property which originally holds for all scalar-valued m-linear forms T : p × × p ? For instance, under what conditions on T : p × × p q, the famous Bohnenblust–Hille inequality and Hardy–Littlewood inequalities for m-linear forms are lifted to T? We prove a general result for nonlinear operators which solves this problem as a very particular case. Our methods encompass Lipschitz operators, m-linear operators and nonlinear operators under mild assumptions. We show that, even in a very nonlinear environment, if the adjoint of T is almost q-summing, then T has the desired property. A straightforward application of our main result provides a generalization of a theorem of S. Kwapień, stated originally for linear operators.

summability property, multiple summing operators, nonlinear summing operators, Kwapień's theorem
Mathematical Subject Classification
Primary: 46G25, 47B10, 47H60, 47H99
Received: 23 May 2023
Revised: 31 July 2023
Accepted: 14 August 2023
Published: 20 January 2024
Daniel Pellegrino
Departamento de Matemática
Universidade Federal da Paraíba
João Pessoa
Joedson Santos
Departamento de Matemática
Universidade Federal da Paraíba
João Pessoa