A-Davis-Wielandt-Berezin radius inequalities

Authors : Verda GÜRDAL, Mualla Birgül HUBAN

Pages : 182-198

Doi:10.31801/cfsuasmas.1107024

View : 13 | Download : 7

Publication Date : 2023-03-30

Article Type : Research Paper

Abstract :We consider operator $V$ on the reproducing kernel Hilbert space $\\mathcal{H}=\\mathcal{H}insert ignore into journalissuearticles values(\\Omega);$ over some set $\\Omega$ with the reproducing kernel $K_{\\mathcal{H},\\lambda}insert ignore into journalissuearticles values(z);=Kinsert ignore into journalissuearticles values(z,\\lambda);$ and define A-Davis-Wielandt-Berezin radius $\\eta_{A}insert ignore into journalissuearticles values(V);$ by the formula $\\eta_{A}insert ignore into journalissuearticles values(V);:=sup\\{\\sqrt{| \\langle Vk_{\\mathcal{H},\\lambda},k_{\\mathcal{H},\\lambda} \\rangle_{A}|^{2}+\\|Vk_{\\mathcal{H},\\lambda}\\|_{A}^{4}}:\\lambda \\in \\Omega\\}$ and $\\tilde{V}$ is the Berezin symbol of $V$ where any positive operator $A$-induces a semi-inner product on $\\mathcal{H}$ is defined by $\\langle x,y \\rangle_{A}=\\langle Ax,y \\rangle$ for $x,y \\in \\mathcal{H}.$ We study equality of the lower bounds for A-Davis-Wielandt-Berezin radius mentioned above. We establish some lower and upper bounds for the A-Davis-Wielandt-Berezin radius of reproducing kernel Hilbert space operators. In addition, we get an upper bound for the A-Davis-Wielandt-Berezin radius of sum of two bounded linear operators.
Keywords : Berezin symbol, A Davis Wielandt Berezin radius, A Berezin number, A Berezin norm, semi inner product, reproducing kernel Hilbert spaces