Strong pseudoconvexity in Banach spaces

Abstract

Having been unclear how to define strong (or strict) pseudoconvexity in the infinite-dimensional and non-smooth boundary context, we take a look at the available literature on strong pseudoconvexity, focusing first in eliminating the need of two degress of smoothness e.g. via distributions. We pass to the infinite-dimensional setting by first seeing a uniform notion of strict pseudoconvexity. Since \(2\)-uniformly PL-convex Banach spaces play an important role as examples with uniformly pseudoconvex unit ball, we briefly show that \(r\)-uniformly convex spaces are \(r\)-uniformly PL-convex, and prove a number of characterizations of \(r\)-uniform PL-convexity.

Journal

Publication date Created: 2017-01-13

Article

ArXiV ID: 1701.03823

License:

http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Custom metadata

ACM classes 32T15, 32C15, 46B25, 32A70

Comments 17 pages

Categories math.CV