Abstract. We present a unified framework to study isometries, with respect to various norms, on $C^{1}([0,1])$, the space of continuously first differentiable functions on the unit interval $[0,1]$. We also discuss continuous deformations of isometry groups induced by perturbations of norms on $C^{1}([0,1])$.

DOI: 10.14232/actasm-017-331-0

AMS Subject Classification (1991): 46E15, 57S10

Keyword(s): isometry, weighted composition operator

Received December 7, 2017 and in final form March 21, 2018. (Registered under 81/2017.)