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Villanueva, Ignacio and Peralta Pereira, Antonio Miguel and Wright, J. D. Maitland and Ylinen, Kari (2010) Weakly compact operators and the strong* topology for a Banach space. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 140 (6). pp. 12491267. ISSN 03082105

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Official URL: http://journals.cambridge.org/action/displayJournal?jid=PRM
Abstract
The strong* topology s_(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x 7! kSxk for bounded linear maps S from X into Hilbert spaces. The wright topology for X, _(X), is a stronger locally convex topology, which may be analogously characterised by taking reflexive Banach spaces in place of Hilbert spaces. For any Banach space Y , a linear map T : X ! Y is known to be weakly compact precisely when T is continuous from the wright topology to the norm topology of Y . The main results deal with conditions for, and consequences of, the coincidence of these two topologies on norm bounded sets. A large class of Banach spaces, including all C_algebras, and more generally, all JB_triples, exhibit this behaviour.
Item Type:  Article 

Uncontrolled Keywords:  Strong* topology; Wright topology; C_algebra; JB_triple; Weakly compact operator 
Subjects:  Sciences > Mathematics > Functional analysis and Operator theory 
ID Code:  12363 
Deposited On:  07 Mar 2011 11:12 
Last Modified:  06 Feb 2014 09:23 
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