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 کاملHigher numerical ranges of matrix polynomials
Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...
متن کاملGeneralized numerical ranges of matrix polynomials
In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.
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: 1981
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1981.95.27