Subspaces of $\displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$
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en
Article de revue
Este ítem está publicado en
Studia Mathematica. 2019, vol. 248, n° 3, p. pp. 233-253.
Instytut Matematyczny - Polska Akademii Nauk
Resumen en inglés
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 ...Leer más >
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 An old (very simple but unpublished so far) construction of bases which are Besselian but not Hilbertian finds a natural place in this development.< Leer menos
Palabras clave en inglés
Besselian and Hilbertian bases
H^p spaces
interpolating sequences.
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