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Rotfel’d type inequalities for norms

2010; Elsevier BV; Volume: 433; Issue: 3 Linguagem: Inglês

10.1016/j.laa.2010.03.029

1873-1856

Eun‐Young Lee,

Numerical methods in inverse problems

In this note, we consider some norm inequalities related to the Rotfel'd Trace InequalityTrf(|A+B|)⩽Trf(|A|)+f(|B|)for concave functions f:[0,∞)→[0,∞) and arbitrary n-by-n matrices. For instance we show that for a large class of non-negative concave functions f(t) and for all symmetric norms we have‖f(|A+B|)‖⩽2‖f(|A|)+f(|B|)‖and we conjecture that this holds for all non-negative concave functions.