A unified Pietsch domination theorem
Geraldo Botelho, Daniel Pellegrino, Pilar Rueda
TL;DR
This paper presents a generalized, abstract version of Pietsch's domination theorem that unifies various known theorems for classes of mappings extending absolutely p-summing operators, emphasizing their algebraic independence.
Contribution
It introduces a unified, algebraically free framework for Pietsch-type domination theorems applicable to broad classes of mappings.
Findings
Unified Pietsch domination theorem for various classes
Dominations are algebraically independent from linearity or multilinearity
Broad applicability to generalized classes of mappings
Abstract
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Banach Space Theory · Optimization and Variational Analysis · Approximation Theory and Sequence Spaces