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3 Bulletin of the Polish Academy of Sciences. Mathematics

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The embeddability of C0 in spaces of operators

Ghenciu I., Lewis P.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 3-4

239-256

Results of Emmanuele and Drewnowski are used to study the containment of c0 in the space Kw* (X*, Y), as well as the complementation of the space Kw* (X*,Y) of w*-w compact operators in the space Lw*(X*, Y) of w*-w operators from X* to Y.

Almost weakly compact operators

Ghenciu I., Lewis P.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

Vol. 54, no 3-4

237-256

Dunford-Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford-Pettis property. The question of whether a space of operators has a Dunford-Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.

Exhaustive submeasures on Boolean rings, Banach lattices and uniform absolute continuity

Huff C., Lewis P.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 3

203-210

A bi-sequential version of a classical theorem dealing with uniform absolute continuity in spaces of measures is extended to the setting of submeasures on a Boolean ring. Applications to spaces of vector measures and Banach lattices are discussed.