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On Weighted Greedy-Type Bases
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Journal Article
On Weighted Greedy-Type Bases
2023
Overview
We study weights for the thresholding greedy algorithm, aiming to extend previous work on sequential weights
ς
on
N
to weights
ω
on
P
(
N
)
.
We revisit major results on weighted greedy-type bases in this new setting including characterizations of
ω
-(almost) greedy bases and the equivalence between
ω
-semi-greedy bases and
ω
-almost greedy bases. Some new results are encountered along the way. For example, we show that there exists an
ω
-greedy unconditional basis that is not
ς
-almost greedy for any weight sequence
ς
.
Moreover, a basis is unconditional if and only if it is
ω
-greedy for some weight
ω
.
Similarly, a basis is quasi-greedy if and only if it is
ω
-almost greedy for some weight
ω
.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
