Some numerical radius inequalities for the \v{C}eby\v{s}ev functional and non-commutative Hilbert space operators

Document Type : Original Article


Jadara University,



In this work, a Gruss inequality for positive Hilbert space operators is
proved. So, 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.