A SURVEY ON LINEAR PRESERVERS OF NUMERICAL RANGES AND RADII
نویسندگان
چکیده
منابع مشابه
A survey on Linear Preservers of Numerical Ranges and Radii
We survey results on linear operators leaving invariant different kinds of generalized numerical ranges and numerical radii.
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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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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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متن کاملSome results on higher numerical ranges and radii of quaternion matrices
Let $n$ and $k$ be two positive integers, $kleq n$ and $A$ be an $n$-square quaternion matrix. In this paper, some results on the $k-$numerical range of $A$ are investigated. Moreover, the notions of $k$-numerical radius, right $k$-spectral radius and $k$-norm of $A$ are introduced, and some of their algebraic properties are studied.
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2001
ISSN: 1027-5487
DOI: 10.11650/twjm/1500574944