Abstract of a paper by Jan-David Hardtke
This is an announcement for the paper "Ball generated property of direct sums of Banach spaces" by Jan-David Hardtke. Abstract: A Banach space $X$ is said to have the ball generated property (BGP) if every closed, bounded, convex subset of $X$ can be written as an intersection of finite unions of closed balls. In 2002 S. Basu proved that the BGP is stable under (infinite) $c_0$- and $\ell^p$-sums for $1<p<\infty$. We will show here that for any absolute, normalised norm $\|\cdot\|_E$ on $\mathbb{R}^2$ satisfying a certain smoothness condition the direct sum $X\oplus_E Y$ of two Banach spaces $X$ and $Y$ with respect to $\|\cdot\|_E$ enjoys the BGP whenever $X$ and $Y$ have the BGP. Archive classification: math.FA Mathematics Subject Classification: 46B20 Remarks: 9 pages Submitted from: hardtke@math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.06224 or http://arXiv.org/abs/1502.06224
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alspach@math.okstate.edu