On almost summing polynomials and multilinear mappings

Abstract

In this article we explore the notion of everywhere almost summing polynomials and define a natural norm which makes this class a Banach polynomial ideal which is a holomorphy type and also coherent and compatible with the notion of almost summing linear operators. Similar results are not valid for the original concept of almost summing polynomials, due to G. Botelho.

Keywords:

• absolutely summing operators
• almost summing operators
• multi-ideals
• multilinear mappings

AMS Subject Classifications::

• Primary: 46G25
• Secondary: 46G20, 47B10, 47H60

Acknowledgements

The authors thank the referee for important suggestions and corrections that substantially improved the presentation of this article. D. Pellegrino is supported by CNPq Grant 301237/2009-3.