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Convexity of the Krein space tracial numerical range and Morse theory
Nakazato, Hiroshi; Bebiano, Natália; Providência, João daIn this paper we present a Krein space convexity theorem on the tracial-numerical range of a matrix. This theorem is the analogue of Westwick's theorem. The proof is an application of Morse theory.
Product of diagonal entries of the unitary orbit of a 3-by-3 normal matrix
Nakazato, Hiroshi; Bebiano, Natália; Providência, João daLet N be a 3×3 normal matrix. We investigate the sets where U(3) is the group of 3×3 unitary matrices and 1[less-than-or-equals, slant]k[less-than-or-equals, slant]3. Geometric properties of these sets are studied, namely, star-shapedness and simple connectedness are investigated. A method for the numerical estimation of is also provided for normal matrices of size 3. ; http://www.sciencedirect.com/science/a...
The J-numerical range of a J-Hermitian matrix and related inequalities
Nakazato, Hiroshi; Bebiano, Natália; Providência, João daRecently, indefinite versions of classical inequalities of Schur, Ky Fan and Rayleigh-Ritz on Hermitian matrices have been obtained for J-Hermitian matrices that are J-unitarily diagonalizable, J=Ir[circle plus operator](-Is),r,s>0. The inequalities were obtained in the context of the theory of numerical ranges of operators on indefinite inner product spaces. In this paper, the subject is revisited, relaxing th...
The numerical range of 2-dimensional Krein spaces operators
Nakazato, Hiroshi; Bebiano, Natália; Providência, João daThe tracial numerical range of operators on a 2-dimensional Krein space is investigated. Results in the vein of those obtained in the context of Hilbert spaces are stated
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