Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590053 | Journal of Functional Analysis | 2014 | 7 Pages |
Abstract
Let H be a separable Hilbert space, A be a Schatten-von Neumann operator in H with the finite norm N2p(A)=[Trace(AAâ)p]1/2p for an integer pâ¥1 and N1(T)=Trace(TTâ)1/2 be the trace norm of a trace operator T. It is proved thatâk=1â|λk(A)|2pâ¤[N2p4p(A)â14N12([A,Aâ]p)]1/2, where λk(A) (k=1,2,...) are the eigenvalues of A, [A,Aâ]p=Ap(Aâ)pâ(Aâ)pAp; Aâ is the adjoint to A. This results refines the classical inequality âk=1â|λk(A)|2pâ¤N2p2p(A). Lower bounds for N1([A,Aâ]p) are also suggested. In addition, if A is a Hilbert-Schmidt operator, we improve the well-known inequalityâk=1â|Imλk(A)|2â¤N22(AI), where AI=(AâAâ)/2i.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Michael Gil',