Some inequalities involving traces of operators

Mehta, C. L. (1968) Some inequalities involving traces of operators Journal of Mathematical Physics, 9 (5). pp. 693-697. ISSN 0022-2488

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We prove that for arbitrary completely continuous operators A1, A2, ···, An and for positive numbers p1, p2, ···, pn with ∑k = 1 npk-1 = 1, the inequalities, |Tr(A1A2···An)|≤ ∏nk=1[Tr(AkAk)½Pk]Pk-1|Trexp(A1 + A2 +···+An)|≤∏nk=1[Trexp{½Pk(Ak + Ak)}]Pk-1 hold. Further if a1, a2, ···, an are the annihilation operators of an N-dimensional harmonic oscillator, m and n are any positive integers, and ρ is a nonnegative definite operator, we prove the inequality |Tr(pai1···aim aj1···ajn| ≤ ∏mk=1[Trp(aik aik)m]½mni=1[Trp(aji aji)n]½n .Some consequences of these inequalities, related results, and some applications to correlation functions of the quantized electromagnetic field are discussed.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:19628
Deposited On:22 Nov 2010 12:16
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