Norm and numerical radius inequalities for sum of operators

In this paper, we present several numerical radius and norm inequalities for sum of Hilbert space operators. These inequalities improve some earlier related inequalities. For an operator T ∈ B(H), we prove thatω2T≤12ωT2+122ωT2+iT*2.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\omega}^{2} \left( T \right) \le \frac{1}{2}\omega \left( {T^{2} } \right) + \frac{1}{{2\sqrt 2 }}\omega \left( {\left| T \right|^{2} + i\left| {T^{\ast} } \right|^{2} } \right) .$$\end{document}