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pro vyhledávání: '"P. Bourin"'
Autor:
Bourin, Jean-Christophe
This is the Habilitation Thesis manuscript presented at Besan\c{c}on on January 5, focusing on Matrix Analysis, Matrix Inequalities and Matrix Decompositions. There are also some topics in (Hilbert space) Operator Theory. The text should be of intere
Externí odkaz:
http://arxiv.org/abs/2307.03064
We establish a sharp inequality between the blocks of positive partitioned matrices and conjecture a triangle type inequality for contractions: Given three contactions A,B,C, we conjecture that the constant c=3/4 is sharp in the triangle inequality |
Externí odkaz:
http://arxiv.org/abs/2307.02034
We study an elementary inequality supporting the classical Hermite-Hadamard inequality in the matrix setting. This leads to a number of interesting matrix inequalities such new Schatten p-norm estimates and new majorization
Comment: To appear in
Comment: To appear in
Externí odkaz:
http://arxiv.org/abs/2201.01210
We prove some eigenvalue inequalities for positive semidefinite matrices partitioned into four blocks. The inradius of the numerical range of the off-diagonal block contributes to these estimates. Some related norm inequalities are given and a conjec
Externí odkaz:
http://arxiv.org/abs/2111.15180
We establish a Pythagorean theorem for the absolute values of the blocks of a partitioned matrix. This leads to a series of remarkable operator inequalities.
Externí odkaz:
http://arxiv.org/abs/2011.13261
Publikováno v:
Internat. J. Math. 29 (2018), no. 12
For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.
Externí odkaz:
http://arxiv.org/abs/2006.09692
We extend some inequalities for normal matrices and positive linear maps related to the Russo-Dye theorem. The results cover the case of some positive linear maps on a von Neumann algebra mapping any nonzero operator to an unbounded operator.
Externí odkaz:
http://arxiv.org/abs/2004.10751
A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten $p$-classes for p>2 is proved
Externí odkaz:
http://arxiv.org/abs/2004.09993
We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range of the off-diagonal block X, especially the distance from 0 to W(X).
Externí odkaz:
http://arxiv.org/abs/2004.07533
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