2008/01/15 by Jarno Talponen, Talponen, Jarno
Mathematics · #46B20 #46B28 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B20 #msc:46B28
paper · pdf · doi:10.48550/arxiv.0801.2314
arxiv created 2008/01/15 · openalex publication_date 2008/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper contains the following results: a) Suppose that X is a non-trivial Banach space and L is a non-empty locally compact Hausdorff space without any isolated points. Then each linear operator T: C0(L,X)→ C0(L,X), whose range does not contain C00 isomorphically, satisfies the Daugavet equality ||I+T||=1+||T||. b) Let Γbe a non-empty set and X, Y be Banach spaces such that X is reflexive and Y does not contain c0 isomorphically. Then any continuous linear operator T: c0(Γ,X)→ Y is weakly compact.