Properties of Derivations Induced by Orthogonal Projections

Abstract

Let Hⁿ be a finite dimensional Hilbert space and δ_P,Q be a generalized derivation induced by the orthogonal projections P and Q. In this study, we have approximated the norm of δ_P,Q by the formula ||δ_P,Q||={Σ|α|²}^1/2+{Σ|β|²}^1/2 and also showed that δ_P,Q is bounded and positive ||δ_P,Q||≥0 whenever P and Q are positive. Finally, we show compactness of δ_P,Q for compact operators P and Q.