Villanueva Díez, 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 1473-7124
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.
|Uncontrolled Keywords:||Strong* topology; W-right topology; C_-algebra; JB_-triple; Weakly compact operator|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
|Deposited On:||07 Mar 2011 12:12|
|Last Modified:||07 Mar 2011 12:12|
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