Two-local isometries on vector-valued differentiable functions

ABSTRACT

In this paper, we investigate the 2-local isometries between the vector-valued differentiable function spaces $C_0^p(X,E)$ and $C_0^q(Y,E)$, where X, Y are open subsets of $\mathbb{R}$ and E is a smooth, strictly convex, reflexive and 2-iso-reflexive Banach space (in particular, when $1\le p<\mathrm{\infty }$ and $p\ne 2$, ${\ell }^p$ satisfies such conditions). We show that such maps can be written as weighted composition operators.

KEYWORDS:

• 2-local isometries
• differentiable functions

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 46B04
• 46E15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by Natural Science Foundation of China [grant numbers 11871303, 11971463, 11671133] and Natural Science Foundation of Shandong Province [grant number ZR2019MA039].