Structure of local Banach spaces of locally convex spaces

1992/04/01 by Jari Taskinen, Taskinen, Jari
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/9204211

openalex publication_date 1992/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a continuous bilinear mapping P: C(I) × C(I) → C(I) can be presented in the form P(f,g) = B((Af)(Ag)), where A and B are bounded linear operators on C(I) and multiplication is defined pointwise, if and only if for all t in I the bilinear form (f,g) -> P(f,g)(t) is integral on C(I) times C(I) and depends in a sense continuously on t. To this end we construct a continuous surjection phi : I → I² admitting a regular averaging operator in the sense of Pelczynski.

Related

• Applications of hypocontinuous bilinear maps in infinite-dimensional differential calculus
• Upper bounds for continuous seminorms and special properties of bilinear maps
• On the global shape of convex functions on locally convex spaces
• Characterizations of strictly convex spaces and proximal uniform normal structure
• Locally uniformly convex norms in Banach spaces and their duals