The numerical range of non-negative operators in Krein spaces

Abstract

We define and characterize the Krein space numerical range W (A) and the Krein space co-numerical range W co (A) of a non-negative operator A in a Krein space. It is shown that the non-zero spectrum of A is contained in the closure of W (A) ∩ W co (A).

Computing the numerical range of Krein space operators

“…The investigation of the numerical range and its generalizations has attracted the interest of researchers from different areas of pure and applied science [4,10], since the concept was born with Toeplitz [26] and Hausdorff [19] in the second decade of the last century. The numerical range of linear operators in an indefinite inner product space is a topic which has deserved the study by some authors; we refer the interested reader to [3,5,6,11,13,14,22,23,24,25]. Ilya Spitkovsky and collaborators published several inspiring papers on the ellipticity of the classical numerical range (see e.g.…”