Subspaces of $\displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$
Langue
en
Article de revue
Ce document a été publié dans
Studia Mathematica. 2019, vol. 248, n° 3, p. pp. 233-253.
Instytut Matematyczny - Polska Akademii Nauk
Résumé en anglais
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 ...Lire la suite >
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 An old (very simple but unpublished so far) construction of bases which are Besselian but not Hilbertian finds a natural place in this development.< Réduire
Mots clés en anglais
Besselian and Hilbertian bases
H^p spaces
interpolating sequences.
Origine
Importé de halUnités de recherche