Characterization of 1-quasi-greedy bases
Fernando Albiac, Jose L. Ansorena
TL;DR
This paper characterizes 1-quasi-greedy bases in Banach spaces, showing they are exactly the unconditional bases with suppression-unconditional constant 1, providing a precise structural understanding.
Contribution
It establishes a necessary and sufficient condition for 1-quasi-greedy bases, linking them to unconditional bases with specific constants.
Findings
1-quasi-greedy bases are unconditional with suppression-unconditional constant 1
Characterization of 1-quasi-greedy bases in Banach spaces
Equivalence between quasi-greedy constant and unconditionality constants
Abstract
We show that a (semi-normalized) basis in a Banach space is quasi-greedy with quasi-greedy constant equal to 1 if and only if it is unconditional with suppression-unconditional constant equal to 1.
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Advanced Operator Algebra Research