On Generalized Numerical Ranges of Quadratic Operators
نویسنده
چکیده
It is shown that the result of Tso-Wu on the elliptical shape of the numerical range of quadratic operators holds also for the essential numerical range. The latter is described quantitatively, and based on that sufficient conditions are established under which the c-numerical range also is an ellipse. Several examples are considered, including singular integral operators with the Cauchy kernel and composition operators.
منابع مشابه
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...
متن کاملTracial Numerical Ranges and Linear Dependence of Operators
Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.
متن کاملEla Tracial Numerical Ranges and Linear Dependence of Operators
Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.
متن کاملElliptical Range Theorems for Generalized Numerical Ranges of Quadratic Operators
The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular, it is shown that for a given quadratic operator, the rank-k numerical range, the essential numerical range, and the q-numerical range are elliptical disks; the c-numerical range is a sum of elliptical disks, and the Davis-Wieland...
متن کاملA mathematically simple method based on denition for computing eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices
In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...
متن کامل