Sharp coincidences for absolutely summing multilinear operators
Daniel Pellegrino
TL;DR
This paper establishes the optimality of certain coincidence theorems for absolutely summing multilinear operators, linking them with multiple summing operators and confirming the sharpness of results derived through complex interpolation.
Contribution
It demonstrates the optimality of known coincidence theorems for absolutely summing multilinear operators and connects these results with the theory of multiple summing operators.
Findings
Proves the optimality of coincidence theorems
Links results with multiple summing operators
Confirms sharpness of complex interpolation results
Abstract
In this note we prove the optimality of a family of known coincidence theorems for absolutely summing multilinear operators. We connect our results with the theory of multiple summing multilinear operators and prove the sharpness of similar results obtained via the complex interpolation method.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Holomorphic and Operator Theory