2018/11/19 by Alomari, Mohammad W.
#15A60 #47A12 #47A30 #47A63 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1811.08025
In this work, a pre-Grüss inequality for positive Hilbert space operators is proved. So that, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound for the numerical radius of the summand of two bounded linear Hilbert space operators is proved. A commutative version is also obtained as well.