Peralta, Antonio M

Villanueva, Ignacio

Wright, J D Maitland

Ylinen, Kari

Proceedings of the Royal Society of Edinburgh Section A Mathematics

English

Aberdeen University Research

[Weakly] compact operators and DF spaces.

A construction of L∞-spaces and related Banach spaces.

C*-algebras and W*-algebras (Springer,

Classical Banach spaces. I. Sequence spaces,

Factoring weakly compact operators.

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Grothendieck’s inequality for JB∗-triples and applications.

Grothendieck’s theorem for non commutative C∗-algebras with an appendix on Grothendieck’s constant.

JB∗-triples have Pelczyn´ski’s property V .

Locally convex spaces

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On the conjugate space of operator algebra.

On the preduals of W ∗-algebras.

On the strong∗ topology of a JBW∗-triple.

On weakly compact operators on C∗-algebras.

Re´sume´ de la the´orie me´trique des produits tensoriels topologiques.

Right topology for Banach spaces and weak compactness.

Sequences and series in Banach spaces,

Some remarks on weak compactness in the dual space of a JB∗-triple.

The dual space of an operator algebra.

The Grothendieck inequality for bilinear forms on C∗-algebras.

The second dual of a JB∗-triple system. In Complex analysis, functional analysis and approximation theory

Topological characterisation of weakly compact operators revisited.

Topological characterisation of weakly compact operators.

Topological vector spaces

Topologies and bornologies determined by operator ideals.

Weak compactness and vector measures.

Weak compactness in the dual space of C∗-algebra.

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

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.I+D Madrid Ciencia y TecnologíaJunta de AndalucíaDepto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu

Peralta Pereira, Antonio Miguel

Villanueva Díez, Ignacio

Wright, J. D. Maitland

Docta Complutense

The strong* topology s*(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x ↦ ‖Sx‖ for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, ρ(X), is a stronger locally convex topology, which may be analogously characterized 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.</jats:p

Antonio M. Peralta

Ignacio Villanueva

J. D. Maitland Wright

Kari Ylinen

Crossref

The strong∗ topology s∗(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x  → ‖Sx ‖ for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, ρ(X), is a stronger locally convex topology, which may be analogously characterized 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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Weakly compact operators and the strong∗ topology for a Banach space

https://aura.abdn.ac.uk/bitstream/2164/2202/1/ProcRoySocEdinB2010_1_.pdf

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

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