On the James constant and B-convexity of Cesàro and Cesàro–Orlicz sequence spaces
By Lech Maligranda, Narin Petrot, Suthep Suantai. 2007
50 citations recorded by the source corpus.
Abstract The classical James constant and the nth James constants, which are measure of B-convexity for the Cesaro sequence spaces ces p and the Cesaro–Orlicz sequence spaces ces M , are calculated. These investigations show that ces p , ces M are not uniformly non-square and even they are not B-convex. Therefore the classical Cesaro sequence spaces ces p are natural examples of reflexive spaces which are not B-convex. Moreover, the James constant for the two-dimensional Cesaro space ces 2 ( 2 ) is calculated.
Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/84b4286f95a199878e3dc3b39f5040bb86d747c8
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In Geometry and Topology
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Structure of Cesàro function spaces (2009, background): “Maligranda, Petrot and Suantai [45] proved that the Cesàro sequence spaces cesp for 1 p ∞ are not uniformly non-square, that is, there are sequences {xn} and {yn} on the unit sphere such that limn→∞ min(‖xn + yn‖c(p),‖xn − yn‖c(p)) = 2.”
- Structure of Cesàro function spaces: a survey (2014, background): “In particular, in 2007 Maligranda–Petrot–Suantai [69] proved that cesp for 1 p ∞ are not uniformly non-square, that is, there are sequences {xn} and {yn} from cesp such that ‖xn‖c(p) = ‖yn‖c(p) = 1 and limn→∞min(‖xn + yn‖c(p), ‖xn − yn‖c(p)) = 2.”