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An envelope for the spectrum of a matrix

100%
Psarrakos P., Tsatsomeros M.
Open Mathematics
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2012
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tom 10
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nr 1
292-302
EN
We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.
2
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Operator inequalities of Jensen type

76%
Moslehian M. S., Mićić J., Kian M.
Topological Algebra and its Applications
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2013
|
tom 1
9-21
EN
We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]
3
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The higher rank numerical range of nonnegative matrices

64%
Aretaki A., Maroulas I.
Open Mathematics
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2013
|
tom 11
|
nr 3
435-446
EN
In this article the rank-k numerical range ∧k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧k (A), we examine their location on the complex plane. Further, an application of this theory to ∧k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C L.
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