Determinantal inequalities for J -accretive dissipative matrices

Authors

DOI:

https://doi.org/10.24193/subbmath.2017.0009

Keywords:

J -accretive dissipative matrix, J -selfadjoint matrix, indefinite inner norm.

Abstract

In this note we determine bounds for the determinant of the sum of two J -accretive dissipative matrices with prescribed spectra.

Mathematics Subject Classification (2010): 46C20, 47A12.

References

Bebiano, N., da Providˆencia, J., A Fiedler-type Theorem for the Determinant of J - Positive matrices, Math. Inequal. Appl., (to appear).

Bebiano, N., Kovacec, A., da Providˆencia, J., The validity of Marcus-de Oliveira Conjecture for essentially Hermitian matrices, Linear Algebra Appl., 197(1994), 411-427.

Bebiano, N., Lemos, R., da Providˆencia, J., Soares, G., Further developments of Furuta inequality of indefinite type, Mathematical Inequalities and Applications, 13(2010), 523- 535.

Bognar, J., Indefinite Inner Product Spaces, Springer, 1974.

Drury, S.W., Cload, B., On the determinantal conjecture of Marcus and de Oliveira, Linear Algebra Appl., 177(1992), 105-109.

Drury, S.W., Essentially Hermitian matrices revisited, Electronic Journal of Linear Algebra, 15(2006), 285-296.

Fiedler, M., The determinant of the sum of Hermitian matrices, Proc. Amer. Math. Soc., 30(1971), 27-31.

Li, C.-K., Poon, Y.-T., Sze, N.-S., Ranks and determinants of the sum of matrices from unitary orbits, Linear and Multilinear Algebra, 56(2008), 108-130.

Marcus, M., Plucker relations and the numerical range, Indiana Univ. Math. J., 22(1973), 1137-1149.

Mc Duff, D., Salamon, D., Introduction to Symplectic Topology, Oxford Matematical Monographs, Clarendon Press, 1998.

Mehta, M.L., Matrix Theory, Selected Topics and Useful Results, Industan Publishing Corporation, New Delhi, 1971.

Nakazato, H., Bebiano, N., da Providˆencia, J., J -orthostochastic matrices of size 3 × 3 and numerical ranges of Krein space operators, Linear Algebra Appl., 407(2005), 211- 232.

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Published

2017-03-01

How to Cite

BEBIANO, N., & DA PROVIDÊNCIA , J. (2017). Determinantal inequalities for J -accretive dissipative matrices. Studia Universitatis Babeș-Bolyai Mathematica, 62(1), 119–125. https://doi.org/10.24193/subbmath.2017.0009

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