Numerical radius of bounded operators with \(\ell^p\)-norm
The authors consider a direct sum of Hilbert spaces \(H\) endowed with a \(p\)-norm, \(1\leq p\leq \infty\), and then introduce for a bounded linear operator \(T\) on \(H\) a set \(W_p(T)\) which they call ``numerical range''. Then they show that many properties known for the classical numerical range of a bounded linear operator in a Hilbert space carry over to \(W_p(T)\). Some of the properties depend on \(p\).
direct sum of a family of Hilbert spaces
scientific article; zbMATH DE number 7625860