Inclusion relations involving thek-numerical range and the essential numerical range
M. S. Jones, H. P. Rogosinski · Linear and Multilinear Algebra · 1994
Let be a complex infinite-dimensional Hilbert space, let be a bounded linear operator on , and let . The k-numerical range of T, denoted by Wk (T), is defined to be the set of points obtained by letting (e1 ,…,ek ) vary over the set of all orthonormal k-tuples in Let We (T) denote the essential numerical range of T. Let and let {βij} i=1 be a sequence of non-negative scalars such that the series converges. In this paper we show that if, and only if,.