$\mathcal F$-bases with brackets and with individual brackets in Banach spaces

Tomasz Kochanek ¹

¹ Institute of Mathematics University of Silesia Bankowa 14 40-007 Katowice, Poland

Studia Mathematica, Tome 211 (2012) no. 3, pp. 259-268

Résumé

We provide a partial answer to the question of Vladimir Kadets whether given an $\mathcal F$-basis of a Banach space $X$, with respect to some filter $\mathcal F\subset\mathcal P(\mathbb N)$, the coordinate functionals are continuous. The answer is positive if the character of $\mathcal F$ is less than $\mathfrak{p}$. In this case every $\mathcal F$-basis is an $M$-basis with brackets which are determined by an element of $\mathcal F$.

Détail

DOI : 10.4064/sm211-3-7

Keywords: provide partial answer question vladimir kadets whether given mathcal f basis banach space respect filter mathcal subset mathcal mathbb coordinate functionals continuous answer positive character mathcal mathfrak every mathcal f basis nbsp m basis brackets which determined element mathcal