# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## First results on spectrally bounded operators

### Tom 152 / 2002

Studia Mathematica 152 (2002), 187-199 MSC: Primary 47B48; Secondary 46B99, 46H40, 47A10, 47L10. DOI: 10.4064/sm152-2-6

#### Streszczenie

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.

#### Autorzy

• M. MathieuDepartment of Pure Mathematics
Queen's University Belfast
Belfast BT7 1NN
Northern Ireland
e-mail
• G. J. SchickDepartment of Pure Mathematics
Queen's University Belfast
Belfast BT7 1NN
Northern Ireland
e-mail

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