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Dual spaces and translation invariant means on group von Neumann algebras

Michael Yin-Hei Cheng (2014)

Studia Mathematica

Let G be a locally compact group. Its dual space, G*, is the set of all extreme points of the set of normalized continuous positive definite functions of G. In the early 1970s, Granirer and Rudin proved independently that if G is amenable as discrete, then G is discrete if and only if all the translation invariant means on L ∞ ( G ) are topologically invariant. In this paper, we define and study G*-translation operators on VN(G) via G* and investigate the problem of the existence of G*-translation invariant...

Dual spaces generated by the interior of the set of norm attaining functionals

Maria D. Acosta, Julio Becerra Guerrero, Manuel Ruiz Galán (2002)

Studia Mathematica

We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the...

Dual spaces of compact operator spaces and the weak Radon-Nikodým property

Keun Young Lee (2012)

Studia Mathematica

We deal with the weak Radon-Nikodým property in connection with the dual space of (X,Y), the space of compact operators from a Banach space X to a Banach space Y. First, under the weak Radon-Nikodým property, we give a representation of that dual. Next, using this representation, we provide some applications to the dual spaces of (X,Y) and w * w ( X * , Y ) , the space of weak*-weakly continuous operators.

Dual spaces of local Morrey-type spaces

Amiran Gogatishvili, Rza Mustafayev (2011)

Czechoslovak Mathematical Journal

In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.

Dual spaces to Orlicz-Lorentz spaces

Anna Kamińska, Karol Leśnik, Yves Raynaud (2014)

Studia Mathematica

For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space Λ φ , w or the sequence space λ φ , w , equipped with either the Luxemburg or Amemiya norms. The first description is via the modular i n f ∫ φ ⁎ ( f * / | g | ) | g | : g ≺ w , where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular ∫ I φ ⁎ ( ( f * ) ⁰ / w ) w ,where (f*)⁰ is Halperin’s level function...

Dualité des espaces de fonctions entières en dimension infinie

Thomas A. W. Dwyer III (1976)

Annales de l'institut Fourier

On étudie ici quelques espaces de fonctions holomorphes dans des domaines localement convexes, ayant comme cas particuliers les espaces de Fock holomorphes. Les espaces duaux sont caractérisés avec la transformation de Fourier-Borel pour des types d’holomorphie appropriés. On montre que ces espaces de fonctions sont de Fréchet-Schwartz (resp. de Silva, resp. nucléaires) quand leurs domaines sont des espaces de Silva (resp. de Fréchet-Schwartz, resp. nucléaires). Les conditions de croissance p -sommable...

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