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General numerical radius inequalities for matrices of operators

100%
Al-Dolat M., Al-Zoubi K., Ali M., Bani-Ahmad F.
Open Mathematics
|
2016
|
tom 14
|
nr 1
109-117
EN
Let Ai ∈ B(H), (i = 1, 2, ..., n), and [...] T=[ 0 ⋯ 0 A 1 ⋮ ⋰ A 2 0 0 ⋰ ⋰ ⋮ A n 0 ⋯ 0 ] $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.
2
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A class of tridiagonal operators associated to some subshifts

100%
Hernández-Becerra C., Itzá-Ortiz B. A.
Open Mathematics
|
2016
|
tom 14
|
nr 1
352-360
EN
We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results by S. N. Chandler-Wilde et al. and R. Hagger, which rely on limit operator techniques, we are able to provide more general results although the closure of the numerical range needs to be taken.
3
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The higher rank numerical range of nonnegative matrices

84%
Aretaki A., Maroulas I.
Open Mathematics
|
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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