A NOTE ON GÂTEAUX DIFFERENTIALS OF HERMITIAN ELEMENTS IN BANACH ALGEBRAS

Gerd Herzog, Christoph Schmoeger
2008 Demonstratio Mathematica  
Let A be a complex unital Banach algebra with unit 1. If a ∈ A is hermitian then we show that a 2 = lim t→0+ t −1 ( 1 + ta 2 − 1), and we give a proof of an inequality due to J. Nieto. 2000 Mathematics Subject Classification: 47A12.
doi:10.1515/dema-2008-0418 fatcat:oxsrl4e2knb5nkl4qglwi6f56i