Symmetric norms and spaces of operators

  title={Symmetric norms and spaces of operators},
  author={Nigel J. Kalton and Fyodor A. Sukochev},
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… 

M-embedded symmetric operator spaces and the derivation problem

Abstract Let ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. Assume that E(0, ∞) is an M-embedded fully symmetric function space having order continuous norm and is

Hermitian operators and isometries on symmetric operator spaces

. Let M be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space H equipped with a

Orbits in symmetric spaces, II

Suppose $E$ is fully symmetric Banach function space on $(0,1)$ or $(0,\infty)$ or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on $f\in E$ so that its orbit

Traces on symmetrically normed operator ideals

Abstract For every symmetrically normed ideal ℰ of compact operators, we give a criterion for the existence of a continuous singular trace on ℰ. We also give a criterion for the existence of a

Higher derivatives of operator functions in ideals of von Neumann algebras

Noncommutative weighted individual ergodic theorems with continuous time

  • V. ChilinS. Litvinov
  • Mathematics
    Infinite Dimensional Analysis, Quantum Probability and Related Topics
  • 2020
We show that ergodic flows in the noncommutative [Formula: see text]-space (associated with a semifinite von Neumann algebra) generated by continuous semigroups of positive Dunford–Schwartz operators

Rademacher averages on noncommutative symmetric spaces




Non-commutative Banach function spaces

In this paper we survey some aspects of the theory of non-commutative Banach function spaces, that is, spaces of measurable operators associated with a semi- finite von Neumann algebra. These spaces

Analytic functions with values in lattices and symmetric spaces of measurable operators

  • Quanhua Xu
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1991
Abstract Let 0 < p,pi ≤ ∞, 0 < q,qi < ∞ (i = 1, 2) such that Let E be a quasi-Banach lattice which fails to contain c0 and whose α-convexity constant is equal to 1 for some 0 < α < ∞. Then for every

Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals

Abstract We present a construction of singular rearrangement invariant functionals on Marcinkiewicz function/operator spaces. The functionals constructed differ from all previous examples in the

Noncommutative Köthe duality

Using techniques drawn from the classical theory of rearrangement invariant Banach function spaces we develop a duality theory in the sense of Kothe for symmetric Banach spaces of measurable

An extremum property of sums of eigenvalues

We present in this note a maximum-minimum characterization of sums like a3+a7+asj where a1> . * * a. are the eigenvalues of a hermitian nXn matrix. The result contains the classic characterization of