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

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DOI

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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     title = {Subadditivity {Inequalities} for {Compact} {Operators}},
     journal = {Canadian mathematical bulletin},
     pages = {25--36},
     year = {2014},
     volume = {57},
     number = {1},
     doi = {10.4153/CMB-2012-009-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-009-9/}
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