Mathematical Sciences: Problems in Banach Spaces

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Professor Casazza will conduct research on several problems in the theory of Banach spaces. They involve (i) uniqueness of unconditional and symmetric structures in finite dimensional spaces, (ii) various forms of the Approximation Property, and (iii) the existence of prime Banach spaces. This award will support research in the geometry of Banach spaces. In finite dimensions, all vector spaces are essentially the same. But in the infinite dimensional situation primarily of interest here, this is far from the case. Banach spaces are infinite dimensional spaces with the additional structure introduced by varying notions of distance between points in the space. Such spaces have wide application in mathematics, both pure and applied.