Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 1 (2018), 222-239.
Stability of average roughness, octahedrality, and strong diameter properties of Banach spaces with respect to absolute sums
We prove that, if Banach spaces and are -average rough, then their direct sum with respect to an absolute norm is -average rough. In particular, for octahedral and and for in , the space is -average rough, which is in general optimal. Another consequence is that for any in there is a Banach space which is exactly -average rough. We give a complete characterization when an absolute sum of two Banach spaces is octahedral or has the strong diameter 2 property. However, among all of the absolute sums, the diametral strong diameter 2 property is stable only for 1- and -sums.
Banach J. Math. Anal., Volume 12, Number 1 (2018), 222-239.
Received: 10 February 2017
Accepted: 15 May 2017
First available in Project Euclid: 5 December 2017
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Haller, Rainis; Langemets, Johann; Nadel, Rihhard. Stability of average roughness, octahedrality, and strong diameter $2$ properties of Banach spaces with respect to absolute sums. Banach J. Math. Anal. 12 (2018), no. 1, 222--239. doi:10.1215/17358787-2017-0040. https://projecteuclid.org/euclid.bjma/1512464420