  Let $H$ be a reflexive, dense, separable, infinite dimensional complex
Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on
$H$. In this paper, we carry out characterizations of norm-attainable operators
in normed spaces. We give conditions for norm-attainability of linear
functionals in Banach spaces, non-power operators on $H$ and elementary
operators. Lastly, we characterize a new notion of norm-attainability for power
operators in normed spaces.
