Abstract
A numerical radius inequality due to Shebrawi and Albadawi says that: If Ai, Bi, Xi are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t (t∈[0, ∞)), then for all r≥1. We give sharper numerical radius inequality which states that: If Ai, Bi, Xi are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t (t∈[0, ∞)), then where . Moreover, we give many numerical radius inequalities which are sharper than related inequalities proved recently, and several applications are given.
Highlights
Hirzallah, Kittaneh and Shebrawi have proved in [8] that: If X ∈ B ( H ), :X + Re X − Im X ≤ w( X ) (4)they proved that: Re X − Im X − X + 2 + 2 ≤ w(X ) (5)they showed that: if X,Y ∈ B ( H ), : w 0 Y
The second lemma follows from the spectral theorem for positive operators and Jensen’s inequality
The first result in this paper is numerical radius inequality which is sharper than the inequality (7)
Summary
We give many numerical radius inequalities which are sharper than related inequalities proved recently, and several applications are given. An important property of the numerical radius norm is its weak unitary invariance, that is, for X ∈ B ( H ) , w(U ∗ XU ) = w( X )
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Advances in Linear Algebra & Matrix Theory
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
