ACTA issues

## Linear isometries on spaces consisting of absolutely continuous functions

Hironao Koshimizu

Acta Sci. Math. (Szeged) 80:3-4(2014), 581-590
77/2012

 Abstract. For $1 \leq p < \infty$, we denote by $\AC ^p [0, 1]$ the space of all absolutely continuous functions on the interval $[0, 1]$ whose derivatives belong to $L^p [0, 1]$. Under the assumption that ${\rm AC}^p [0, 1]$ is equipped with the norm $\| f \|_\sigma = |f(0)| + \| f' \|_L^p$ or $\| f \|_m = \max\{ |f(0)|, \| f' \|_L^p \}$, we characterize the surjective linear isometries on ${\rm AC}^p [0, 1]$. DOI: 10.14232/actasm-012-327-3 AMS Subject Classification (1991): 46B04; 46E15 Keyword(s): linear isometry, absolutely continuous function Received September 24, 2012, and in revised form December 3, 2012. (Registered under 77/2012.)