Norm attaining operators into locally asymptotically midpoint uniformly convex Banach spaces

Abstract

We prove that if $Y$ is a locally asymptotically midpoint uniformly convex Banach space which has either a normalized, symmetric basic sequence that is not equivalent to the unit vector basis in ${\ell }_1$, or a normalized sequence with upper p-estimates for some $p>1$, then $Y$ does not satisfy Lindenstrauss' property B.

5 pages