Abstract of a paper by Tomasz Kochanek
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
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