Document Type : Original Manuscript
Authors
Department of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord, Iran.
Abstract
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.
Keywords
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