On inequalities for A-numerical radius of operators Article Swipe

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Mathematics Hilbert space Diagonal Operator matrix Operator (biology) Diagonal matrix RADIUS Spectral radius Numerical range Operator norm Product (mathematics) Matrix (chemical analysis) Upper and lower bounds Pure mathematics Algebra over a field Mathematical analysis Eigenvalues and eigenvectors Geometry Quantum mechanics Computer security Computer science Repressor Materials science Chemistry Composite material Physics Biochemistry Gene Transcription factor

Pintu Bhunia , Kallol Paul , Raj Kumar Nayak ·

YOU? · · 2019 · Open Access · · OA: W3021117839

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ Inequalities are presented concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in [A. Zamani. A-Numerical radius inequalities for semi-Hilbertian space operators. Linear Algebra Appl., 578:159--183, 2019]. Also, some inequalities are obtained for $B$-numerical radius of $2\times 2$ operator matrices, where $B$ is the $2\times 2$ diagonal operator matrix whose diagonal entries are $A$. Further, upper bounds are obtained for $A$-numerical radius for product of operators, which improve on the existing bounds.