This is an announcement for the paper "$\mathcal F$-bases with individual brackets in Banach spaces" by Tomasz Kochanek.

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 with individual brackets is an $M$-basis with brackets determined by a set from $\mathcal F$.

Archive classification: math.FA

Submitted from: t.kania@lancaster.ac.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1207.3097

or

http://arXiv.org/abs/1207.3097