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THE VON NEUMANN SCHATTEN CLASSES
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adjoint algebraic multiplicities Banach space bounded linear functional bounded linear operator chain of closed closed invariant subspace closed subspace compact linear operator completes the proof complex Banach space complex number continuous chain Corollary counted according cp(A defined denote Dokl easily verified element entire function equation exists finite rank finite-dimensional follows from Lemma follows from Theorem Fredholm determinant Fredholm theory Furthermore Hence Hilbert space implies inequality integral operator invariant each subspace invariant subspace isometric isomorphism leaves invariant lim inf linear operator acting mapping Math matrix non-zero eigenvalues null space operators of finite orthogonal orthonormal basis orthonormal sequence orthonormal system polar decomposition polynomials positive integer positive real number principal vectors prove quasi-nilpotent operator result satisfied scalars self-adjoint operator sequence of non-zero shows simple chain skew-adjoint summable superdiagonal integral Suppose totally ordered trace class operator unit vector zero