RT Journal Article
T1 Weakly compact operators and the strong* topology for a Banach space
A1 Villanueva, Ignacio
A1 Peralta Pereira, Antonio Miguel
A1 Wright, J. D. Maitland
A1 Ylinen, Kari
AB 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.
PB Cambridge University Press
SN 0308-2105
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/41910
UL https://hdl.handle.net/20.500.14352/41910
LA eng
NO I+D MCYT
NO Junta de Andalucía
NO I+D MCYT
DS Docta Complutense
RD 8 may 2024