Dear all, The next Banach spaces webinar is on Friday October 23 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Przemyslaw Wojtaszczyk, Institut of Mathematics Polish Academy of Sciences Title: Quasi-greedy bases in $p$-Banach spaces Abstract: This talk is based on the paper F. Albiac, J.L. Ansorena and P.W. \emph{On certain subspaces of $\ell_p$ for $0<p\le 1$ and their applications to conditional quasi-greedy bases in $p$-Banach spaces} Mathematische Annalen--available on line. We construct new quasi-greedy bases in $\ell_p$ and in the kernels of certain quotient maps from $\ell_p $ onto $L_p$, $0<p\leq 1$ and study its properties. We note that all the kernels we study are isomorphic; we denote this space as ${\mathfrak l }_p$ . We show that there is continuum of non-equivalent quasi-greedy bases in $\ell_p$ and ${\mathfrak l }_p$ and we study the conditionality of those bases. For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari