Generic non-extendability and total unboundedness in function spaces

2018/11/11 by Vassili Nestoridis, Nestoridis, V., Aristomenis G. Siskakis +5
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1811.04408

Abstract

For a function space X(\OO) satisfying weak assumptions we prove that the generic function in X(\OO) is totally unbounded, hence non-extendable. We provide several examples of such spaces; they are mainly localized versions of classical function spaces and intersections of them.

Related

• Localized versions of function spaces and generic results
• Uniform boundedness in function spaces
• Non extendability from any side of the domain of definition as a generic property of smooth or simply continuous functions on an analytic curve
• Non-extendability of holomorphic functions with bounded or continuously extendable derivatives
• Boundedness properties in function spaces