[Settfa] Tuesday 23/06, <span style="font-family:arial; font-size:14px">Tommaso Russo</span>

[kubis at math.cas.cz]

 ------------------------------------------------------------------------- 

 Tuesday 23rd June, 10:00am 
 
  Place: IM in konírna 

 
    ------------------------------------------------------------------------- 

 Speaker:Tommaso Russo, CVUT / IM CAS
 Title: Asplund spaces and norming Markushevich bases

 Abstract  

 
The first existence result for normingMarkuševi? bases (M-bases, for short) in Banach spaces
 
is perhaps due toMarkuševi?, who proved that every separable Banach space admits a 1-norming M-basis.
 
After the introduction of projectional resolutions of the identity, it became clear that such bases
 
alsoexist in every reflexive Banach space.
 

 
A natural problem at the time was then to characterise those (non-separable)Banach spaces
 
that admit a norming M-basis. Perhaps the main question, due originally to John and Zizler
 
and that was solved very recently by P.Hájek, was whether every weakly compactly generated
 
(WCG) Banach spaceadmits a norming M-basis.
 

 
In the converse direction, it was asked by Gilles Godefroyif an Asplund space with a norming M-basis
 
is necessarily WCG. In the talk, based on a joint work withP. Hájek, J. Somaglia, and S. Todor?evi?

we shall discuss our recent negative answer to the latter question.



 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .