arXiv subjects
Publications and source records attributed to Rajna Rajić.
It is shown that Birkhoff-James orthogonality knows everything about the smooth norms in reflexive Banach spaces and can also compute the dimensions of the underlying normed spaces.
Let $\mathcal A$ be a unital $C^*$-algebra with the unit $e$. We consider the elements $a\in \mathcal A$ which are Roberts orthogonal to the unit $e$. We obtain a characterization of this orthogonality in terms of the Davis--Wielandt shell of $a$ and show that, for certain classes of elements of $\mathcal A$, the Roberts orthogonality of $a$ and $e$ is equivalent to the symmetry of the numerical range of $a$ with respect to the origin.