The numerical range of a tridiagonal operator
The authors study the numerical range of several (infinite or finite) tridiagonal matrices. As a sample, we mention here the tridiagonal operator defined by \(Ae_j = e_{j-1} + r^je_{j+1}\), with respect to the standard orthonormal basis \(\{e_n\}\) of \(\ell^2(\mathbb N)\). Such tridiagonal operators are related to some Rogers-Ramanujan identities.
scientific article; zbMATH DE number 5804462