Isometric shifts on (c⊕X)∞
Let c be the set of all convergent sequences with the sup norm and X a strictly convex Banach space. Let Q be the natural projection from (c⊕X)∞ to X and let T be an isometric shift on (c⊕X)∞. We prove the following:. (1)The restriction of Q T to X is a surjective isometry.(2)T maps c into c and the restriction of T to c is an isometric shift. We also show that the space (c⊕l1)∞ admits an isometric shift. © 2011 Elsevier Inc.
Journal of Mathematical Analysis and Applications
Lin, P. (2011). Isometric shifts on (c⊕X)∞. Journal of Mathematical Analysis and Applications, 384 (2), 198-203. https://doi.org/10.1016/j.jmaa.2011.03.071