The numerical range of linear operators on the 2-dimensional Krein space

A theoretical investigation of S-Numerical Range with the respect to a family of projections

“…The set ( ) is well-known set in which each of the sets ( ) and ( ) are convex sets. The relationships between the sets ( ) and ( ) are described in (Bebiano, N., Lemos, R., Da providencia, J. and Soares, 2005) and (Nakazato,H., Bebiano, N. & D A Providencia, J., 2011). According to Bayasgalan (Bayasgalan, 1991), the set ( ) is convex if is nonsingular and indefinite.…”

Some results on S-numerical range of operator matrices

“…We also define the related sets It is well-known that each of the sets and is convex set and, as , decomposes into at most two convex subsets. In (Bebiano et al, 2004) boundary generating curves, corners and computer generation of the Krein space numerical range are investigated, in (Bebiano et al, 2005, Nakazato et al, 2011relations between the sets and are discussed. The set and have been investigated.…”