Norm Properties of $S$-Universal Operators

Abstract

We investigate the norm properties of a generalized derivation on a norm ideal $\mathcal{J}$ in $\mathcal{B}(H)$, the algebra of bounded linear operators on a Hilbert space $H$. Specifically, we extend the concept of $S-$universality from the inner derivation to the generalized derivation context, establish the necessary conditions for the attainment of the optimal value of the circumdiameters of numerical ranges and the spectra of two bounded linear operators on $H$. Moreover, we characterize the antidistance from an operator to its similarity orbit in terms of the circumdiameters, norms, numerical and spectra radii of a pair of $S$-universal operators.

Keywords

• spectrum
• numerical range
• circumdiameter
• similarity orbit
• antidistance
• norms;
• norm ideals
• normaloid
• spectraloid operators