$\mathcal F$-bases with brackets and with individual brackets in Banach spaces
Volume 211 / 2012
Studia Mathematica 211 (2012), 259-268
MSC: Primary 46B15.
DOI: 10.4064/sm211-3-7
Abstract
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 $\mathcal F$.
