Farzaneh Gorjizadeh - Department of Pure Mathematics, University of Shahrekord, P.O. Box ۱۱۵, Shahrekord, Iran.
Noha Eftekhari - Department of Pure Mathematics, University of Shahrekord, P.O. Box ۱۱۵, Shahrekord, Iran.

‎This work aims to introduce and investigate a preordering in B(\mathcal{H}),‎ ‎the Banach space of all bounded linear operators defined on a complex‎ ‎Hilbert space \mathcal{H}. It is called strong majorization and denoted by S\prec_{s}T, for‎ ‎S,T\in B(\mathcal{H}). The strong majorization follows majorization defined by Barnes‎, ‎but not vice versa‎. ‎If S\prec_{s}T, then S inherits some properties of T. ‎‎‎‎ The strong majorization will be extended for the d-tuple of operators in B(\mathcal{H})^{d} and‎ ‎is called joint strong majorization denoted by S\prec_{js}T, for S,T\in B(\mathcal{H})^{d}. We show that‎ ‎some properties of strong majorization are satisfied for joint strong majorization‎.

Strong majorization, Hilbert space‎, Positive operator