Intersection properties for generalized numerical ranges*
M. S. Jones, B. Nashvadian-Bakhsh, H. P. Rogosinski · Linear and Multilinear Algebra · 1993
Let be a complex infinite-dimensional Hilbert space, and let be a bounded linear operator on Let The C-numerical range of T, denoted by WC (T), is defined to be the set of scalars obtained by letting (e 1,…,ek ) vary over the set of all orthonormal k-tuples in If C=diag(1/k,…,1/k), then WC (T) reduces to the k-numerical range of T, denoted by Wk (T). Let the essential numerical range of T be denoted by We (T). In this paper we first show that . We also show that the essential numerical range of T, the C-numerical range of T, and the k-numerical range of T are related by where