• DOI:10.1515/CRELLE.2008.059
• Corpus ID: 37112035

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}
}

• N. Kalton, F. Sukochev
• Published 2008
• Mathematics

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 new concept of uniform Hardy-Littlewood majorization; completeness also requires a new proof. We also give the analogous results for operator spaces modelled on a semifinite von Neumann algebra with a normal faithful semi-finite trace.