Year: 2017
Type: preprint
Abstract: In this paper, we consider the question of contractivity vs. complete contractivity for domains in $\mathbb{C}^2$, which are unit balls with respect to some norm. We show that for a large class of Reinhardt domains, the corresponding Banach spaces do not have Property P, which implies that there exists contractive homomorphisms on these domains which are not completely contractive. At the end, we present a simple proof of the fact that the complex Banach spaces $(\mathbb{C}^2,\|\cdot\|_{\infty})$ and $(\mathbb{C}^3,\|\cdot\|_{\infty})$ have Property P.
Source: arXiv (Cornell University)
Author: Ray, Samya Kumar
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2575192393