On Jensen's Multiplicative Inequality for Positive Convex Functions of Selfadjoint Operators in Hilbert Spaces

Document Type : Original Article


Mathematics, College of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia.


We obtain some multiplicative refinements and reverses of Jensen's inequality for positive convex/concave functions of selfadjoint operators in Hilbert spaces. Natural applications for power and exponential functions are provided.