
TL;DR
This paper introduces variable exponent ll^p spaces with unique local geometric properties, providing new examples of Banach spaces that have a 1-unconditional basis, expanding the understanding of their structure.
Contribution
It presents a novel class of variable exponent ll^p spaces with specific local control of geometric properties, not rearrangement-invariant, and constructs examples with a 1-unconditional basis.
Findings
Spaces have good local geometric control
Examples of Banach spaces with 1-unconditional basis
Spaces are typically not rearrangement-invariant
Abstract
We introduce and study certain type of variable exponent \ell^p spaces. These spaces will typically not be rearrangement-invariant but instead they enjoy a good local control of some geometric properties. We obtain some interesting examples of Banach spaces with a 1-unconditional basis.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Holomorphic and Operator Theory
