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On A-numerical radius inequalities for $2 \times 2$ operator matrices
- Publication Year :
- 2020
-
Abstract
- Let ($\mathcal{H}, \langle . , .\rangle )$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\|T\|_A$ be the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbertian space $(\mathcal{H}, \langle .,.\rangle_A),$ where $\langle x, y\rangle_A:=\langle Ax, y\rangle$ for all $x,y\in \mathcal{H}$. In this article, we establish several upper and lower bounds for $B$-numerical radius of $2\times 2$ operator matrices, where $B=\begin{bmatrix} A & 0 0 & A \end{bmatrix}$. Further, we prove some refinements of earlier $A$-numerical radius inequalities for operators.<br />Comment: 16 pages
- Subjects :
- Mathematics - Functional Analysis
Primary 47A05, Secondary 46C05, 47B65, 47A12
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2004.07494
- Document Type :
- Working Paper