Author:
Albiac Fernando,Ansorena José L.,Bello Glenier,Wojtaszczyk Przemysław
Abstract
AbstractWe prove that the sequence spaces $$\ell _p\oplus \ell _q$$
ℓ
p
⊕
ℓ
q
and the spaces of infinite matrices $$\ell _p(\ell _q)$$
ℓ
p
(
ℓ
q
)
, $$\ell _q(\ell _p)$$
ℓ
q
(
ℓ
p
)
and $$(\bigoplus _{n=1}^\infty \ell _p^n)_{\ell _q}$$
(
⨁
n
=
1
∞
ℓ
p
n
)
ℓ
q
, which are isomorphic to certain Besov spaces, have an almost greedy basis whenever $$0<p<1<q<\infty $$
0
<
p
<
1
<
q
<
∞
. More precisely, we custom-build almost greedy bases in such a way that the Lebesgue parameters grow in a prescribed manner. Our arguments critically depend on the extension of the Dilworth–Kalton–Kutzarova method from Dilworth et al. (Stud Math 159(1):67–101, 2003), which was originally designed for constructing almost greedy bases in Banach spaces, to make it valid for direct sums of mixed-normed spaces with nonlocally convex components. Additionally, we prove that the fundamental functions of all almost greedy bases of these spaces grow as $$(m^{1/q})_{m=1}^\infty $$
(
m
1
/
q
)
m
=
1
∞
.
Funder
Universidad Pública de Navarra
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,General Mathematics,Analysis