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Featured researches published by G. Soares.


Linear & Multilinear Algebra | 2004

On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space

Natália Bebiano; R. Lemos; J. da Providência; G. Soares

In this article, numerical ranges associated with operators on an indefinite inner product space are investigated. Boundary generating curves, corners, shapes and computer generations of these sets are studied. In particular, the Murnaghan–Kippenhahn theorem for the classical numerical range is generalized.


Linear & Multilinear Algebra | 2001

Linear operators preserving the numerical range (radius) on triangular matrices

Chi-Kwong Li; Peter Šemrl; G. Soares

We characterize those linear operators on triangular or diagonal matrices preserving the numerical range or radius.


Linear & Multilinear Algebra | 2013

Extremal case in Marcus–Oliveira conjecture and beyond

Alexander E. Guterman; R. Lemos; G. Soares

For A, C ∈ M n the C-determinantal range of A is the following set on the complex plane ▵ C (A) = {det(A − UCU*): UU* = I n }. For normal matrices A and C with eigenvalues α1, … , α n and γ1, … , γ n , respectively, Marcus [M. Marcus, Derivations, Plücker relations and the numerical range, Indiana Univ. Math. J. 22 (1973), pp. 1137–1149] and Oliveira [G.N. de Oliveira, Normal matrices (research problem), Linear Multilinear Algebra 12 (1982), pp. 153–154] conjectured that ▵ C (A) is a subset of the convex hull of the points , σ ∈ S n , where S n is the symmetric group of degree n. We investigate the extremal set of matrices for which the equality holds in the Marcus–Oliveira conjecture. We illustrate the use of the obtained results by two different applications. The first one deals with the equality case between the radius of ▵ C (A) and the radius of the convex hull of the points z σ, σ ∈ S n . The second one is the characterization of additive Frobenius endomorphisms for the determinantal range or radius on the space M n and on its real subspace of Hermitian matrices.


Applied Mathematics and Computation | 2016

On the C-determinantal range for special classes of matrices

Alexander E. Guterman; R. Lemos; G. Soares

Let A and C be square complex matrices of size n, the C-determinantal range of A is the subset of the complex plane { det ( A - U C U * ) : U U * = I n } . If A, C are both Hermitian matrices, then by a result of Fiedler (1971) 11 this set is a real line segment.In our paper we study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two well-known results on this topic. The first result is due to Li concerning the C-numerical range of a Hermitian matrix, see Condition 5.1?(a) in Li, (1994) 20. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et?al. (2008) 21, Theorem 3.3).


Linear Algebra and its Applications | 2005

On the geometry of numerical ranges in spaces with an indefinite inner product

Natália Bebiano; R. Lemos; J. da Providência; G. Soares


Linear Algebra and its Applications | 2005

Inequalities for J-Hermitian matrices

Natália Bebiano; Hiroshi Nakazato; J. da Providência; R. Lemos; G. Soares


Mathematical Inequalities & Applications | 2010

Further developments of Furuta inequality of indefinite type

Natália Bebiano; R. Lemos; João da Providência; G. Soares


Mathematical Inequalities & Applications | 2012

Operator inequalities for J-contractions

Natália Bebiano; R. Lemos; João da Providência; G. Soares


The Journal of Advanced Research in Applied Mathematics | 2009

A Note on Indefinite Chaotic Order

Natália Bebiano; R. Lemos; J. da Providência; G. Soares


Archive | 2009

Inequalities for J-contractions involving the alpha-power mean

G. Soares

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R. Lemos

University of Aveiro

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Peter Šemrl

University of Ljubljana

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