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 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.
