Generalized A-Numerical Radius of Operators and Related Inequalities

Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{\theta \in {R}}}\; N_A\left( \frac{e^{i\theta }T+e^{-i\theta }T^{\sharp _A}}{2}\right) \end{aligned}$$ where $$T^{\sharp _A}$$ stands for distinguished A-adjoint T. In this article, we focus development several inequalities. We also develop bounds sum operators.