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SOME NUMERICAL RADIUS INEQUALITIES FOR SEMI-HILBERT SPACE OPERATORS

  • Feki, Kais (Faculty of Economic Sciences and Management of Mahdia University of Monastir, Laboratory Physics-Mathematics and Applications (LR/13/ES-22) Faculty of Sciences of Sfax University of Sfax)
  • 투고 : 2021.01.07
  • 심사 : 2021.04.12
  • 발행 : 2021.11.01

초록

Let A be a positive bounded linear operator acting on a complex Hilbert space (𝓗, ⟨·,·⟩). Let ωA(T) and ║T║A denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space (𝓗, ⟨·,·⟩A), respectively, where ⟨x, y⟩A := ⟨Ax, y⟩ for all x, y ∈ 𝓗. In this paper, we show with different techniques from that used by Kittaneh in [24] that $$\frac{1}{4}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A{\leq}{\omega}^2_A(T){\leq}\frac{1}{2}{\parallel}T^{{\sharp}_A}T+TT^{{\sharp}_A}{\parallel}_A.$$ Here T#A denotes a distinguished A-adjoint operator of T. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the 𝔸-numerical radius of the operator matrix $\(\array{I&T\\0&-I}\)$ where 𝔸 = diag(A, A). In addition, several A-numerical radius inequalities for semi-Hilbert space operators are also established.

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참고문헌

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