Properties of Spectrally Bounded Compact Elementary Operators

Abstract

Spectrally bounded compact elementary operators on dense irreducible subalgebras of C ∗ -algebras are characterized. Also, it is shown that left multiplications, right multiplications, generalized derivations and basic elementary operators are spec trally bounded compact elementary operators. Furthermore, several properties of spectrally bounded compact elementary operators such as completeness, convergence, continuity and total boundedness in a general Banach setting are outlined.