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ON THE PRODUCT OF DERIVATIONS IN BANACH ALGEBRAS
- Mathematical Proceedings of the Royal Irish Academy
- Royal Irish Academy
- Volume 109A, Number 2, October 2009
- pp. 201-212
- 10.1353/mpr.2009.0007
- Article
- Additional Information
Abstract
Abstract:
The purpose of this paper is to study derivations d, g defined on a complex Banach algebra A such that the spectrum σ(dg(x)) is finite for all x Є A. In particular we show that if the algebra A is semisimple, then dg(x)³ lies in the socle of A for every x Є A.
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