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.
Alomari, M. (2021). Some numerical radius inequalities for the \v{C}eby\v{s}ev functional and non-commutative Hilbert space operators. Khayyam Journal of Mathematics, 7(1), 96-108. doi: 10.22034/kjm.2020.205545.1598
MLA
Mohammad W. Alomari. "Some numerical radius inequalities for the \v{C}eby\v{s}ev functional and non-commutative Hilbert space operators". Khayyam Journal of Mathematics, 7, 1, 2021, 96-108. doi: 10.22034/kjm.2020.205545.1598
HARVARD
Alomari, M. (2021). 'Some numerical radius inequalities for the \v{C}eby\v{s}ev functional and non-commutative Hilbert space operators', Khayyam Journal of Mathematics, 7(1), pp. 96-108. doi: 10.22034/kjm.2020.205545.1598
VANCOUVER
Alomari, M. Some numerical radius inequalities for the \v{C}eby\v{s}ev functional and non-commutative Hilbert space operators. Khayyam Journal of Mathematics, 2021; 7(1): 96-108. doi: 10.22034/kjm.2020.205545.1598