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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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