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

2012 ◽  
Vol 210 (3) ◽  
pp. 247-260 ◽  
Author(s):  
Keun Young Lee
Keyword(s):  
Compact Operator ◽  
Operator Spaces ◽  
Dual Spaces ◽  
Nikodym Property

Dual spaces ofJB *-triples and the Radon-Nikodym property

1991 ◽  
Vol 208 (1) ◽  
pp. 327-334 ◽  
Author(s):  
L. J. Bunce ◽  
C. -H. Chu
Keyword(s):  
Dual Spaces ◽  
Nikodym Property

scholarly journals Connections Between Metric Characterizations of Superreflexivity and the Radon–Nikodým Property for Dual Banach Spaces

2015 ◽  
Vol 58 (1) ◽  
pp. 150-157 ◽  
Author(s):  
Mikhail I. Ostrovskii
Keyword(s):  
Banach Spaces ◽  
Present Author ◽  
Converse Statement ◽  
Dual Spaces ◽  
Nikodym Property

AbstractJohnson and Schechtman (2009) characterized superreflexivity in terms of finite diamond graphs. The present author characterized the Radon–Nikodým property (RNP) for dual spaces in terms of the infinite diamond. This paper is devoted to further study of relations between metric characterizations of superreflexivity and the RNP for dual spaces. The main result is that finite subsets of any setMwhose embeddability characterizes the RNP for dual spaces, characterize superreflexivity. It is also observed that the converse statement does not hold and thatM=l2is a counterexample.

scholarly journals Priestley duality for MV-algebras and beyond

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wesley Fussner ◽  
Mai Gehrke ◽  
Samuel J. van Gool ◽  
Vincenzo Marra
Keyword(s):  
Large Class ◽  
Order Conditions ◽  
Enriched Environment ◽  
Priestley Duality ◽  
Distributive Lattices ◽  
First Order ◽  
Dual Spaces ◽  
Binary Operations ◽  
New Perspective ◽  
Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

scholarly journals Convolutors on $${\mathcal S}_{\omega }({\mathbb R}^N)$$

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Angela A. Albanese ◽  
Claudio Mele
Keyword(s):  
Fourier Transform ◽  
Dual Space ◽  
Strong Operator ◽  
Dual Spaces ◽  
Structure Theorems ◽  
The Fourier Transform ◽  
Decreasing Functions

AbstractIn this paper we continue the study of the spaces $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) and $${\mathcal O}_{C,\omega }({\mathbb R}^N)$$ O C , ω ( R N ) undertaken in Albanese and Mele (J Pseudo-Differ Oper Appl, 2021). We determine new representations of such spaces and we give some structure theorems for their dual spaces. Furthermore, we show that $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) is the space of convolutors of the space $${\mathcal S}_\omega ({\mathbb R}^N)$$ S ω ( R N ) of the $$\omega $$ ω -ultradifferentiable rapidly decreasing functions of Beurling type (in the sense of Braun, Meise and Taylor) and of its dual space $${\mathcal S}'_\omega ({\mathbb R}^N)$$ S ω ′ ( R N ) . We also establish that the Fourier transform is an isomorphism from $${\mathcal O}'_{C,\omega }({\mathbb R}^N)$$ O C , ω ′ ( R N ) onto $${\mathcal O}_{M,\omega }({\mathbb R}^N)$$ O M , ω ( R N ) . In particular, we prove that this isomorphism is topological when the former space is endowed with the strong operator lc-topology induced by $${\mathcal L}_b({\mathcal S}_\omega ({\mathbb R}^N))$$ L b ( S ω ( R N ) ) and the last space is endowed with its natural lc-topology.

Conformally self-dual spaces and Maxwell's equations

1984 ◽  
Vol 106 (3) ◽  
pp. 125-129 ◽  
Author(s):  
C.P. Boyer ◽  
J.F. Plebański
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Dual Spaces

On the Radon-Nikodym Property in Jordan Triples

1987 ◽  
Vol 99 (3) ◽  
pp. 462 ◽  
Author(s):  
Cho-Ho Chu ◽  
Bruno Iochum
Keyword(s):  
Nikodym Property

Dunford-Pettis operators and the Radon-Nikodym property

1988 ◽  
Vol 50 (2) ◽  
pp. 183-188 ◽  
Author(s):  
V. Caselles
Keyword(s):  
Nikodym Property
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