Lower Bounds for Eigenvalues of Schatten-von Neumann Operators
نویسندگان
چکیده
Let Sp be the Schatten-von Neumann ideal of compact operators equipped with the norm Np(·). For an A ∈ Sp (1 < p <∞), the inequality [ ∞ ∑ k=1 |Reλk(A)| ] 1 p + bp [ ∞ ∑ k=1 | Imλk(A)| ] 1 p ≥ Np(AR)− bpNp(AI) (bp = const. > 0) is derived, where λj(A) (j = 1, 2, . . . ) are the eigenvalues of A, AI = (A − A∗)/2i and AR = (A + A∗)/2. The suggested approach is based on some relations between the real and imaginary Hermitian components of quasinilpotent operators.
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