Subspaces of $displaystyle H^{p}$ linearly homeomorphic to $l^{p}.$Report as inadecuate




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1 IMB - Institut de Mathématiques de Bordeaux 2 ICJ - Institut Camille Jordan Villeurbanne

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 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 An old very simple but unpublished so far construction of bases which are Besselian but not Hilbertian finds a natural place in this development.

Keywords : interpolating sequences. H^p spaces Besselian and Hilbertian bases





Author: Eric Amar - Bernard Chevreau - Isabelle Chalendar -

Source: https://hal.archives-ouvertes.fr/



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