On the James constant and B-convexity of Cesàro and Cesàro–Orlicz sequence spaces

The classical James constant and the nth James constants, which are measure of B-convexity for the Cesàro sequence spaces cesp and the Cesàro–Orlicz sequence spaces cesM, are calculated. These investigations show that cesp, cesM are not uniformly non-square and even they are not B-convex. Therefore the classical Cesàro sequence spaces cesp are natural examples of reflexive spaces which are not B-convex. Moreover, the James constant for the two-dimensional Cesàro space ces(2) 2 is calculated. © 2006 Elsevier Inc. All rights reserved.