%0 Journal Article
%A Villanueva, Ignacio
%A Peralta Pereira, Antonio Miguel
%A Wright, J. D. Maitland
%A Ylinen, Kari
%T Weakly compact operators and the strong* topology for a Banach space
%D 2010
%@ 0308-2105
%U https://hdl.handle.net/20.500.14352/41910
%X 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.
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