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Application of ( L ) sets to some classes of operators

Kamal El Fahri, Nabil Machrafi, Jawad H'michane, Aziz Elbour (2016)

Mathematica Bohemica

The paper contains some applications of the notion of Ł sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order ( L ) -Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an ( L ) sets. As a sequence characterization of such operators, we see that an operator T : X E from a Banach space into a Banach lattice is order Ł -Dunford-Pettis, if and only if | T ( x n ) | 0 for σ ( E , E ' ) for every weakly null...

Applications of spherical designs to Banach space theory

Hermann König (2004)

Banach Center Publications

Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or p -spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants...

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