Weighted composition operators of C₀(X)'s

1996/07/30 by Jeang, Jyh-Shyang, Wong, Ngai-Ching
#46E15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9607212

Abstract

In this paper, we prove that into isometries and disjointness preserving linear maps from C₀(X) into C₀(Y) are essentially weighted composition operators Tf = h⋅ f∘φ for some continuous map φ and some continuous scalar-valued function h.

Related

• Into isometries of C₀(X,E)'s
• Stability and instability of weighted composition operators
• Weight-preserving isomorphisms between spaces of continuous functions: The scalar case
• Automatic continuity and weighted composition operators between spaces of vector-valued differentiable functions
• A note on composition operators between weighted spaces of smooth functions