# Symmetric norms and spaces of operators

@inproceedings{Kalton2008SymmetricNA, title={Symmetric norms and spaces of operators}, author={Nigel J. Kalton and Fyodor A. Sukochev}, year={2008} }

Abstract We show that if (E, ∥ · ∥ E ) is a symmetric Banach sequence space then the corresponding space of operators on a separable Hilbert space, defined by if and only if , is a Banach space under the norm . Although this was proved for finite-dimensional spaces by von Neumann in 1937, it has never been established in complete generality in infinite-dimensional spaces; previous proofs have used the stronger hypothesis of full symmetry on E. The proof that is a norm requires the apparently…

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