Document Type : Original Manuscript


Department of Pure Mathematics, University of Shahrekord, P.O. Box 115, 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.


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