NEW MAJORIZATION FOR BOUNDED LINEAR OPERATORS IN HILBERT SPACES | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 2، فروردین 2024، صفحه 1-12 اصل مقاله (145.98 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11318.1564 | ||
| نویسندگان | ||
| Farzaneh Gorjizadeh؛ Noha Eftekhari* | ||
| Department of Pure Mathematics, University of Shahrekord, P.O. Box 115, Shahrekord, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Strong majorization؛ Hilbert space؛ Positive operator | ||
| مراجع | ||
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