Abstract

Let A=( ⁣ ⁣A00A ⁣ ⁣)\mathbf{A=}\left(\!\! \begin{array}{cc} A & 0 \\ 0 & A \end{array}\!\! \right) be a 2×22\times 2 diagonal operator matrix whose each diagonal entry is a positive bounded linear operator AA acting on a complex Hilbert space H{\mathcal{H}}. Let T,ST,S and RR be bounded linear operators on H{\mathcal{H}} admitting AA-adjoints, where TT and RR are AA-positive. By considering an A\mathbf{A}-positive 2×22 \times 2 operator matrix ( ⁣ ⁣TS♯ASR ⁣ ⁣)\left(\!\!\begin{array}{cc}T & S^{^{\sharp _{A}}} \\S & R \end{array}\!\!\right), we develop several upper bounds for the AA-numerical radius of SS. Applying these upper bounds we obtain new AA-numerical radius bounds for the product and the sum of arbitrary operators which admit AA-adjoints. Related other inequalities are also derived.

Author information

Contact details are reproduced from the original publication and may be historical.

Kallol Paul

Dept. of Mathematics, Jadavpur University, Kolkata, West Bengal, India

kalloldada@gmail.com

Keywords

  • A-numerical radius
  • positive operator
  • seminorm
  • semi-inner product

Mathematics Subject Classification

47A05, 47A12, 47A30, 47B15

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Suggested citation

M. Guesba, P. Bhunia, K. Paul. “A-Numerical Radius of Semi-Hilbert Space Operators.” Journal of Convex Analysis 31 (2024), No. 1, 227–242. https://doi.org/10.68381/jca31013

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.