∂ λ f (s) , (1.1.1) f Σ = λ∈Λ ∂ λ f ∞ and (1.1.2) f M = max λ∈Λ ∂ λ f ∞ . (1.1.3) Cambern [3] showed that the surjective linear isometries on (C 1 ([0, 1], C), • C ) are weighted composition operators. Then Pathak [5] extended the result to (C p ([0, 1], C), • C ). On the other hand, Jarosz and Pathak [9] characterized onto linear isometries on (C 1 [0, 1], • Σ ) and (C 1 [0, 1], • M ). Botelho and Jamison [6] considered a vector-valued continuously differentiable function space, where E is a finite-dimensional Hilbert space and showed that all onto linear isometries on such function spaces are weighted composition operators. Subsequently, Li and Wang [7] extended their result to vector-valued differentiable function space which vanish at infinity (C p 0 (Q, E), • C ), where Q is an open subset of R m and E is a reflexive and strictly convex Banach space. Recently, Li et al. [8] characterized onto linear isometries on (C p 0 (Q, E), • Σ ) where Q ⊆ R is open and E is a strictly convex Banach space E with dimension greater than 1. In this thesis, we aim to provide a unified approach for the norms
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.