Dear all,
The next Banach spaces webinar is on Friday August 28 9AM CDT (e.g., Dallas, TX time). Please join us at
https://unt.zoom.us/j/512907580
Speaker: Tommaso Russo (Czech Academy of Sciences and Czech Technical University in Prague)
Title: Asplund Banach spaces with norming Markuševič bases
Abstract The first existence result for norming Markuševič bases (M-bases, for short) in Banach spaces is perhaps due to Markuševič, 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 also exist in every reflexive Banach space.
In order to understand the strength of the said notion, 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 space admits a norming M-basis.
In the converse direction, it was asked by Gilles Godefroy if an Asplund space with a norming M-basis is necessarily WCG. In the talk, based on a joint work with P. Hájek, J. Somaglia, and S. Todorčević, we shall discuss our recent negative answer to the latter question. Moreover, the construction yields an interesting example of a scattered compact space that also solves a question due to Wiesław Kubiś and Arkady Leiderman.
* For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach
Upcoming schedule
September 4: Mary Angelica Tursi (UIUC)
Thank you, and best regards,
Bunyamin Sari