Coherence and compatibility: a stronger approach

ABSTRACT

In this work, we present new definitions of coherence and compatibility of classes of multilinear mappings and homogeneous polynomials. These new definitions are more strict than the ones proposed before. We begin the analysis of these new definitions by searching the similarities with the previous approaches. Then, we move on to a more practical analysis, using a number of different classes of multilinear mappings and homogeneous polynomials to check the limits of these new definitions and to suggest that they have a wide range of applications.

Keywords:

• Banach spaces
• multilinear operators
• multi-ideals
• symmetric ideals

2010 Mathematics Subject:

• 47L22
• 46G25
• 47L20
• 47B10

Acknowledgments

We thank the anonymous referee for her/his careful reading of the manuscript and for the suggestions that improved the final presentation of the paper. We also thank Professor Geraldo Botelho for his helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Fabricio Santos was supported by a CAPES doctoral scholarship and Ewerton R. Torres was supported by a CAPES postdoctoral scholarship.