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Displaying 561 – 580 of 1072

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The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of c 0

L. Drewnowski, G. Emmanuele (1993)

Studia Mathematica

Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of c 0 . Then the Bochner space L 1 ( m ; X ) is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.

The product of a function and a Boehmian

Dennis Nemzer (1993)

Colloquium Mathematicae

Let A be the class of all real-analytic functions and β the class of all Boehmians. We show that there is no continuous operation on β which is ordinary multiplication when restricted to A.

The product of distributions on R m

Cheng Lin-Zhi, Brian Fisher (1992)

Commentationes Mathematicae Universitatis Carolinae

The fixed infinitely differentiable function ρ ( x ) is such that { n ρ ( n x ) } is a regular sequence converging to the Dirac delta function δ . The function δ 𝐧 ( 𝐱 ) , with 𝐱 = ( x 1 , , x m ) is defined by δ 𝐧 ( 𝐱 ) = n 1 ρ ( n 1 x 1 ) n m ρ ( n m x m ) . The product f g of two distributions f and g in 𝒟 m ' is the distribution h defined by error n 1 error n m f 𝐧 g 𝐧 , φ = h , φ , provided this neutrix limit exists for all φ ( 𝐱 ) = φ 1 ( x 1 ) φ m ( x m ) , where f 𝐧 = f * δ 𝐧 and g 𝐧 = g * δ 𝐧 .

The projective limit functor for spectra of webbed spaces

L. Frerick, D. Kunkle, J. Wengenroth (2003)

Studia Mathematica

We study Palamodov's derived projective limit functor Proj¹ for projective spectra consisting of webbed locally convex spaces introduced by Wilde. This class contains almost all locally convex spaces appearing in analysis. We provide a natural characterization for the vanishing of Proj¹ which generalizes and unifies results of Palamodov and Retakh for spectra of Fréchet and (LB)-spaces. We thus obtain a general tool for solving surjectivity problems in analysis.

The projective tensor product (II): the Radon-Nikodym property.

Joe Diestel, Jan Fourie, Johan Swart (2006)

RACSAM

In this paper we discuss the problem of when the projective tensor product of two Banach spaces has the Radon-Nikodym property. We give a detailed exposition of the famous examples of Jean Bourgain and Gilles Pisier showing that there are Banach spaces X and Y such that each has the Radon-Nikodym property but for which their projective tensor product does not; this result depends on the classical theory of absolutely summing, integral and nuclear operators, as well as the famous Grothendieck inequality...

The property ( β ) of Orlicz-Bochner sequence spaces

Paweł Kolwicz (2001)

Commentationes Mathematicae Universitatis Carolinae

A characterization of property ( β ) of an arbitrary Banach space is given. Next it is proved that the Orlicz-Bochner sequence space l Φ ( X ) has the property ( β ) if and only if both spaces l Φ and X have it also. In particular the Lebesgue-Bochner sequence space l p ( X ) has the property ( β ) iff X has the property ( β ) . As a corollary we also obtain a theorem proved directly in [5] which states that in Orlicz sequence spaces equipped with the Luxemburg norm the property ( β ) , nearly uniform convexity, the drop property and...

Currently displaying 561 – 580 of 1072