Polynomial numerical index with respect to a norm-one polynomial
F\'abio J. Bertoloto, Elisa R. Santos
TL;DR
This paper introduces a new polynomial numerical index for pairs of Banach spaces relative to a norm-one polynomial, extending previous concepts and exploring its properties with examples.
Contribution
It generalizes existing numerical index concepts to polynomials and investigates their properties in Banach spaces.
Findings
The polynomial numerical index extends previous operator-based indices.
Properties of the polynomial numerical index are characterized.
Examples illustrate the application of the new index.
Abstract
In this paper, we introduce the polynomial numerical index of a pair of Banach spaces with respect to a norm-one polynomial. This index generalizes the concept of polynomial numerical index defined by Y. S. Choi et al. in 2006 and extends to polynomials the notion of numerical index with respect to an operator, introduced by M. A. Ardalani in 2014. We investigate several properties of this index and present examples.
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Approximation Theory and Sequence Spaces