The algebraic numerical range as a spectral set in Banach algebras
The algebraic numerical range as a spectral set in Banach algebras
We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix algebras and provide an absolute constant in the case of complex $2\times2$-matrices with the induced …