Numerical radius inequalitiesPaljanin, Selma (Avtor) Drnovšek, Roman (Mentor) numerical rangenumerical radiusreverse inequalitiesassociated functionalsEuclidean operator radiusWe introduce some basic theory about numerical range and numerical radius. Basic inequalities for numerical radius which involve one operator and basic inequalities which involve product of two commutative operators are studied. We then introduce more complex numerical radius inequalities for one operator, finding some upper bounds for the nonnegative quantites $\|T\|-w(T)$ and $\|T\|^2-w^2(T)$ under different assumptions for operator $T$, including inequalities for some associated functionals. We establish new inequalities for composite operators generated by some operators $A$ and $B$ under certain assumptions on $A$ and $B$. We introduce a functional $\mu(A,B)$ associated with two operators and study upper bounds for nonnegative differences $\mu(A,B)-w(B^{\ast}A)$ and $\mu^2(A,B)-w^2(B^{\ast}A)$. Finally, we introduce Euclidean Operator Radius and extend some earlier results to Euclidean radius of two operators.20222022-03-17 08:15:02Magistrsko delo/naloga135506sl