G-invariant norms and G(c)-radii
Let V be a finite-dimensional inner product space over F \((=C\) or R), and let G be a closed subgroup of the group of unitary operators on V. A norm \(\| \cdot \|\) on V is said to be G-invariant if \(\| g(x)\| =\| x\|\) for all \(g\in G\), \(x\in V\). The authors discuss the general properties of a G-invariant norm. Linear operators on V that preserve G-invariant norms are also investigated. Several open problems are mentioned.
scientific article; zbMATH DE number 4189936
scientific article