A refinement of A-Buzano inequality and applications to A-numerical radius inequalities

Let A be a positive bounded operator on a Hilbert space H and let ‖T‖A, wA(T), and mA(T) denote the A-operator seminorm, the A-numerical radius, and the A-minimum modulus of an operator T in the semi-Hilbertian space (H,‖⋅‖A), respectively. In this paper, we present new improvements of certain A-Cau...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2024-09, Vol.697, p.32-48
Main Authors: Kittaneh, Fuad, Zamani, Ali
Format: Article
Language:English
Subjects:
A-numerical radius
Inequality
Positive operator
Semi-inner product
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let A be a positive bounded operator on a Hilbert space H and let ‖T‖A, wA(T), and mA(T) denote the A-operator seminorm, the A-numerical radius, and the A-minimum modulus of an operator T in the semi-Hilbertian space (H,‖⋅‖A), respectively. In this paper, we present new improvements of certain A-Cauchy–Schwarz type inequalities and as applications of our results, we provide refinements of some A-numerical radius inequalities for semi-Hilbertian space operators. It is shown, among other inequalities, thatwA(T)≤(1−12infλ∈C⁡mA2(I−λT))‖T‖A, where I is the identity operator on H. A refinement of the triangle inequality for semi-Hilbertian space operators is also given.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2023.02.020