Some norm inequalities for accretive Hilbert space operators

Baharak Moosavi; Mohsen Shah Hosseini

doi:10.56754/0719-0646.2602.327

DOI:

https://doi.org/10.56754/0719-0646.2602.327

Abstract

New norm inequalities for accretive operators on Hilbert space are given. Among other inequalities, we prove that if \(A, B \in \mathbb{B(H)}\) and \(B\) is self-adjoint and also \(C_{m,M}(iAB)\) is accretive, then

\begin{eqnarray*}
\frac{4 \sqrt{Mm}}{M+m} \Vert AB\Vert \leq \omega(AB-BA^*),\end{eqnarray*}
where \(M\) and \(m\) are positive real numbers with \(M > m\) and \(C_{m,M}(A) = (A^* - mI)(MI - A)\). Also, we show that if \(C_{m,M}(A)\) is accretive and \((M-m) \leq k \Vert A \Vert\), then

\begin{eqnarray*}
\omega(AB) \leq ( 2 + k)\omega(A)\omega(B).\end{eqnarray*}

Keywords

Bounded linear operator , Hilbert space , norm inequality , numerical radius

Mathematics Subject Classification:

47A12 , 47A30 , 47A63

Baharak Moosavi Department of Mathematics, Safadasht Branch, Islamic Azad University, Tehran, Iran. https://orcid.org/0000-0002-4643-4096
Mohsen Shah Hosseini Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran. https://orcid.org/0000-0001-9458-7196

Pages: 327–340
Date Published: 2024-08-09
Vol. 26 No. 2 (2024)

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