On some numerical characteristics of operators

Abstract

We investigate some numerical characteristics of Toeplitz operators including the numerical range, maximal numerical range and maximal Berezin set. Further, we establish an inequality for the Berezin number of an arbitrary operator on the Hardy–Hilbert space of the unit disc.

Keywords

• Berezin symbol
• Berezin number
• Maximal numerical range
• Maximal Berezin set
• Toeplitz operator
• Numerical range
• Normal operator