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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,385 - 1,405 (21page)
- DOI
- 10.4134/JKMS.j210017
이용수
초록· 키워드
오류제보하기
Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$. Let $\omega_A(T)$ and ${\|T\|}_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbert space $\big(\mathcal{H}, {\langle \cdot, \cdot\rangle}_A\big)$, respectively, where ${\langle x, y\rangle}_A := \langle Ax, y\rangle$ for all $x, y\in\mathcal{H}$. In this paper, we show with different techniques from that used by Kittaneh in \cite{FK} that \begin{equation*} \tfrac{1}{4}\|T^{\sharp_A} T+TT^{\sharp_A}\|_A\le \omega_A^2\left(T\right) \le \tfrac{1}{2}\|T^{\sharp_A} T+TT^{\sharp_A}\|_A. \end{equation*} Here $T^{\sharp_A}$ denotes a distinguished $A$-adjoint operator of $T$. Moreover, a considerable improvement of the above inequalities is proved. This allows us to compute the $\mathbb{A}$-numerical radius of the operator matrix $\left(\begin{smallmatrix} I&T\\ 0&-I \end{smallmatrix}\right)$ where $\mathbb{A}= \text{diag}(A,A)$. In addition, several $A$-numerical radius inequalities for semi-Hilbert space operators are also established.
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참고문헌 (27)
참고문헌 신청
Amer Abu-Omar / 2015 / Upper and lower bounds for the numerical radius with an application to involution operators / Rocky Mountain Journal of Mathematics 45(4):1163~1173
Amer Abu-Omar / 2015 / Numerical radius inequalities for nXn operator matrices / Linear Algebra and its Applications 468:18~26
M. Laura Arias / 2008 / Partial isometries in semi-Hilbertian spaces / Linear Algebra and its Applications 428(7):1460~1475
M. Laura Arias / 2008 / Metric Properties of Projections in Semi-Hilbertian Spaces / Integral Equations and Operator Theory 62(1):11~28
M. L. Arias / 2009 / Lifting properties in operator ranges / Acta Sci. Math. (Szeged) 75(3-4):635~653
Amer Abu-Omar / 2015 / Numerical radius inequalities for nXn operator matrices / Linear Algebra and its Applications 468:18~26
M. Laura Arias / 2008 / Partial isometries in semi-Hilbertian spaces / Linear Algebra and its Applications 428(7):1460~1475
M. Laura Arias / 2008 / Metric Properties of Projections in Semi-Hilbertian Spaces / Integral Equations and Operator Theory 62(1):11~28
M. L. Arias / 2009 / Lifting properties in operator ranges / Acta Sci. Math. (Szeged) 75(3-4):635~653
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