Subspaces of $\displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$
Language
en
Article de revue
This item was published in
Studia Mathematica. 2019, vol. 248, n° 3, p. pp. 233-253.
Instytut Matematyczny - Polska Akademii Nauk
English Abstract
We present two fast constructions of weak*-copies of ℓ ∞ in H ∞ and show that such copies are necessarily weak*-complemented. Moreover, via a Paley-Wiener type of stability theorem for bases, a connection can be made in ...Read more >
We present two fast constructions of weak*-copies of ℓ ∞ in H ∞ and show that such copies are necessarily weak*-complemented. Moreover, via a Paley-Wiener type of stability theorem for bases, a connection can be made in some cases between the two types of construction, via interpolating sequences (in fact these are at the basis of the second construction). Our approach has natural generalizations where H ∞ is replaced by an arbitrary dual space and ℓ ∞ by ℓ p (1 ≤ p ≤ ∞) relying on the notions of generalized interpolating sequence and bounded linear extension. An old (very simple but unpublished so far) construction of bases which are Besselian but not Hilbertian finds a natural place in this development.Read less <
English Keywords
Besselian and Hilbertian bases
H^p spaces
interpolating sequences.
Origin
Hal imported