First results on spectrally bounded operators
Volume 152 / 2002
Studia Mathematica 152 (2002), 187-199
MSC: Primary 47B48; Secondary 46B99, 46H40, 47A10, 47L10.
DOI: 10.4064/sm152-2-6
Abstract
A linear mapping $T$ from a subspace $E$ of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant $M\geq 0$ such that $r(Tx)\leq Mr(x)$ for all $x\in E$, where $r(\cdot )$ denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.
