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

Volume 211 / 2012

Tomasz Kochanek Studia Mathematica 211 (2012), 259-268 MSC: Primary 46B15. DOI: 10.4064/sm211-3-7


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 $\mathcal F$.


  • Tomasz KochanekInstitute of Mathematics
    University of Silesia
    Bankowa 14
    40-007 Katowice, Poland

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