[Settfa] Seminar, 5 September, 10:00, IM CAS, Konirna

[Wieslaw Kubis]

Dear all,

Below are details for tomorrow's seminar. We apologize for sending it 
late, for some strange reasons the automatic announcement didn't go out.

Best,

Wieslaw


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Jerzy Kąkol

Faculty of Mathematics, A. Mickiewicz University, Poznań, Poland

About the problem of Banach and Mazur from the 1930s. Classical and new 
results

One of the famous unsolved problems of functional analysis asks (Banach 
Mazurs problem (1932) if every infinite dimensional Banach space E can 
be mapped by a continuous linear operator onto an infinite dimensional 
separable Banach space. This problem is known under the name : Separable 
quotient problem. For many concrete Banach spaces the answer is 
positive, for example, reflexive Banach spaces, or even weakly compactly 
generated Banach spaces. Argyros, Dodos and Kanellopoulos, proved that 
every dual Banach space has a separable quotient. On the other hand, 
Rosenthal showed that all Banach spaces C(X) of continuous (real-valued) 
functions on X have a quotient isomorphic to c0 or l2. We provide 
several useful methods to examine which Banach spaces admit a separable 
quotient, and the same problem will be studied for spaces Cp(X) with the 
pointwise topology. The talk gathers also quite new results. A 
connection with Efimov compact spaces X will be also discussed.