منابع مشابه
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×...
متن کاملThe Ninth Workshop on Numerical Ranges and Numerical Radii
In this talk I will discuss some instances in quantum computing where numerical range techniques arise. I will also try to formulate some open problems. Elliptical range theorems for generalized numerical ranges of quadratic operators Speaker Chi-Kwong Li, William and Mary, [email protected] Co-authors Yiu-Tung Poon, Iowa State University, [email protected]; Nung-Sing Sze, University of Connect...
متن کاملOn Generalized Numerical Ranges of Quadratic Operators
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...
متن کاملCorners of multidimensional numerical ranges
The n-dimensional numerical range of a densely defined linear operator T on a complex Hilbert space H is the set of vectors in Cn of the form (〈Te1, e1〉, . . . , 〈Ten, en〉), where e1, . . . , en is an orthonormal system in H, consisting of vectors from the domain of T . We prove that the components of every corner point of the n-dimensional numerical range are eigenvalues of T .
متن کاملNumerical ranges of composition operators
Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 i...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1978
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1978.77.303