Variant versions of the Lewent type determinantal inequality

  title={Variant versions of the Lewent type determinantal inequality},
  author={Ali Morassaei},
In this paper, we present a refinement of the Lewent determinantal inequality and show that the following inequality holds det IH +A1 IH −A1 + det IH +An IH −An − n ∑ j=1 λj det ( IH +Aj IH −Aj ) ≥ det (IH +A1 IH −A1 )( IH +An IH −An ) n ∏ j=1 ( IH +Aj IH −Aj )−λj , where Aj ∈ B(H), 0 ≤ Aj < IH, Aj ’s are trace class operators and A1 ≤ Aj ≤ An (j = 1, . . . , n) and ∑n j=1 λj = 1, λj ≥ 0 (j = 1, . . . , n). In addition, we present some new versions of the Lewent type determinantal… 



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