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When

Start: 09/25/2013 - 4:15pm

End : 09/25/2013 - 5:15pm

End : 09/25/2013 - 5:15pm

Category

Colloquium

Speaker

Mehmet Orhon, University of New Hampshire

Abstract

Abstract: The subject of this talk concerns three areas of Functional Analysis: Banach space geometry, Banach lattices, and Banach -modules, where represents the Banach algebra of continuous (real or complex-valued) functions on a compact Hausdorff space .

A Banach space is called reflexive if, as a set, it is equal to its bidual ′′. Typical examples of non-reflexive spaces are (sequences convergent to zero) and (absolutely summable sequences). A classical result of Banach space geometry states that “A Banach space with unconditional basis is reflexive if and only if it does not contain any closed subspace that is isomorphic to either or ,” (James, 1950). In 1968 Lozanovsky proved that a Banach lattice is reflexive if and only if it does not contain any closed subspace that is isomorphic to either or .

It is known that a Banach -module with one generator is representable as a Banach lattice. Using this fact and some additional Banach space geometry results in Banach lattice theory, we extend the reflexivity criterion of Lozanovsky to finitely generated Banach -modules; in particular, a finitely generated Banach -module is reflexive if and only if it does not contain any closed subspace that is isomorphic to either or .

Where

Davidson Lecture Hall, Claremont McKenna College

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Orhon.pdf | 139.37 KB |