Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces.

The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h (λ) = ∑ k = 0 ∞ a k λ k and its modified version h a (λ) = ∑ k = 0 ∞ | a k | λ k . The convergence of h (λ) is assumed on the open disk D (0 , R) , where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities. [ABSTRACT FROM AUTHOR]