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On Besselian Schauder bases in \(\ell_ p(E)\). (English) Zbl 0531.46009
By complex interpolation and tensor products, Schauder bases are constructed of the Banach sequence spaces \(\ell_ p(E)\). In a general result, we study the Besselian property of the basis, and if E is assumed to be the \(L_ p\) (Lebesgue) and \(S_ p\) (von Neumann-Schatten) space, we obtain inequalities for the coefficient functionals associated to the basis which generalise other results given by Hausdorff-Young and Gohberg-Marcus. Finally, we construct non-Besselian and conditional bases of \(\ell_ p(E)\).
MSC:
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E40 Spaces of vector- and operator-valued functions
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References:
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