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Grant 201/07/0394     1.1.2007 - 31.12.2009
Grantor: Grant Agency of Czech Republic (GACR)

Infinite dimensional analysis

We propose to work on problems in several areas of infinite dimensional analysis. Regarding the structure of Banach spaces, does every Banach space contain a monotone basic sequence? What is the optimal value of boundedness constant for an M-basis of a general Banach space. We conjecture the answer is 2. What are the structural consequences of a long Schauder basis. In connection with renorming theory, find an example of a LUR renormable space with M-basis, but no strong M-basis. Clarify the relationship between the separable complementation property and PRI. Clarify the relationship between Szlenk index and dentability index, for which there exists a nonconstructive proof of dependence. Try to generalize the Szlenk index technique in the context of topologies framented by a metric and beyond. In particular, as an application, does there exist a universal Corson compact space?

 Main investigator:

Hájek Petr

 IM team members:  
Fabian Marián
John Kamil
Zizler Václav