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Weakly compact operators and the strong* topology for a Banach space

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. 1249-1267. ISSN 0308-2105

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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 w-right 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 w-right 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; W-right 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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