Ela Krein Spaces Numerical Ranges and Their Computer Generation

Shapes and computer generation of numerical ranges of Krein space operators

Krein Space Numerical Ranges: Compressions and Dilations

A criterion for the numerical range of a linear operator acting in a Krein space to be a two-component hyperbolical disc is given, using the concept of support function. A characterization of the Krein space numerical range as a union of hyperbolical discs is obtained by a reduction to the two-dimensional case. We revisit a famous result of Ando concerning the inclusion relation W (A) ⊆ W (B) o...

Ela Numerical Ranges of Quadratic Operators in Spaces with an Indefinite Metric

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.

Remarks on generalized numerical ranges of operators on indefinite inner product spaces

Numerical ranges associated to operators on an indefinite inner product space are investigated. Boundary generating curves, shapes, corners and computer generation of these sets are studied. Some final remarks present an interesting relation between these sets and numerical ranges of operators arising in quantum mechanics.

Some results on higher numerical ranges and radii of quaternion matrices

‎Let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $A$ be an $n$-square quaternion matrix‎. ‎In this paper‎, ‎some results on the $k-$numerical range of $A$ are investigated‎. ‎Moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $A$ are introduced‎, ‎and some of their algebraic properties are studied‎.