Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces

Multiplicities, Boundary Points, and Joint Numerical Ranges

The multiplicity of a point in the joint numerical range W (A1, A2, A3) ⊆ R is studied for n×n Hermitian matrices A1, A2, A3. The relative interior points of W (A1, A2, A3) have multiplicity greater than or equal to n−2. The lower bound n−2 is best possible. Extreme points and sharp points are studied. Similar study is given to the convex set V (A) := {xT Ax : x ∈ R, x x = 1} ⊆ C, where A ∈ Cn×...

A Henrici Theorem for Joint Spectra of Commuting Matrices

A version of Henrici's classical perturbation theorem for eigenvalues of matrices is obtained for joint spectra of commuting tuples of matrices. The approach involves Clifford algebra techniques introduced by Mcintosh and Pryde.

Adjoints, Numerical Ranges, and Spectra of Operators on Locally Convex Spaces

Spectra, Norms and Numerical Ranges of Generalized Quadratic Operators

A bounded linear operator acting on a Hilbert space is a generalized quadratic operator if it has an operator matrix of the form [ aI cT dT ∗ bI ] . It reduces to a quadratic operator if d = 0. In this paper, spectra, norms, and various kinds of numerical ranges of generalized quadratic operators are determined. Some operator inequalities are also obtained. In particular, it is shown that for a...

Eigenvalues and Ranges for Perturbations of Nonlinear Accretive and Monotone Operators in Banach Spaces

Various eigenvalue and range results are given for perturbations of m-accretive and maximal monotone operators. The eigenvalue results improve and extend some recent results by Guan and Kartsatos, while the range theorem gives an affirmative answer to a recent problem of Kartsatos.