Multiplicative preservers of higher-dimensional numerical ranges
نویسندگان
چکیده
منابع مشابه
Multiplicative Preservers of C-Numerical Ranges and Radii
Multiplicative preservers of C-numerical ranges and radii on certain groups and semigroups of complex n × n matrices are characterized. The general and special linear groups are considered, as well as the semigroups of matrices having ranks not exceeding k, with k fixed in advance. For a fixed C, it turns out that typically the multiplicative preservers of the C-numerical range (or radius) have...
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Let Mn be the semigroup of n× n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in Mn including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λk(A) is the rank-k numerical range and rk(A) is the rank-k numerical radius of A ∈ Mn. Multiplicative maps φ : S → Mn satisfying rk(φ(A)...
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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...
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We survey results on linear operators leaving invariant different kinds of generalized numerical ranges and numerical radii.
متن کاملInclusion regions for numerical ranges and Linear Preservers
There has been considerable interest in studying inclusion regions for numerical ranges. It is in fact very useful in knowing inclusion regions for W (A). For example, it is well known (see [4, Chapter 1]) that W (A) ⊆ IR if and only if A = A∗; W (A) ⊆ [0,∞) if and only if A is positive semidefinite; andW (A) ⊆ (0,∞) if and only if A is positive definite. Moreover, Ando [1] (see also [2]) showe...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.11.007