Geodesic
Subadditivity Inequalities for Compact Operators
Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 25-36

Voir la notice de l'article provenant de la source Cambridge University Press

Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon $ term. It does not seem possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon $ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also emphasizes matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings.
DOI : 10.4153/CMB-2012-009-9
Mots-clés : 47A63, 15A45, concave or convex function, Hilbert space, unitary orbits, compact operators, compressions, matrix inequalities 
Bourin, Jean-Christophe; Harada, Tetsuo; Lee, Eun-Young. Subadditivity Inequalities for Compact Operators. Canadian mathematical bulletin, Tome 57 (2014) no. 1, pp. 25-36. doi: 10.4153/CMB-2012-009-9
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[1] [1] Aujla, J. S. and Bourin, J.-C., Eigenvalue inequalities for convex and log-convex functions. Linear Algebra Appl. 424 (2007), 25–35. Google Scholar | DOI

[2] [2] Bourin, J.-C., Harada, T. and Lee, E.-Y., Strict type inequalities for Hilbert space operators. Unpublished manuscript. Google Scholar

[3] [3] Bourin, J.-C. and Hiai, F., Norm and anti-norm inequalities for positive semi-definite matrices. Internat. J. Math. 63 (2011), 1121–1138. Google Scholar | DOI

[4] [4] Bourin, J.-C., Jensen and Minkowski inequalities for operator means and anti-norms. Preprint, arxiv:1106.2213v3. Google Scholar

[5] [5] Bourin, J.-C. and Lee, E.-Y., Concave functions of positive operators, sums, and congruences. J. Operator Theory 63 (2010), 151–157. Google Scholar

[6] [6] Bourin, J.-C. and Lee, E.-Y., Unitary orbits of Hermitian operators with convex or concave functions. Preprint, arxiv:1109.2384v1. Google Scholar

[7] [7] Harada, T. and Kosaki, H., On equality condition for trace Jensen inequality in semi-finite vonNeumann algebras. Internat. J. Math. 19 (2008), 481–501. Google Scholar | DOI

[8] [8] Rotfel'd, S. Ju., The singular values of a sum of completely continuous operators. In: Topics in Mathematical Physics 3 (1969), 73–78. Google Scholar

[9] [9] Simon, B., Trace Ideals and Their Applications. Second edition, Amer. Math. Soc., Providence, RI, 2005. Google Scholar

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