Fully symmetric operator spaces

1992 ◽  
Vol 15 (6) ◽  
pp. 942-972 ◽  
Author(s):  
Peter G. Dodds ◽  
Theresa K. Dodds ◽  
Ben de Pagter
Keyword(s):  
Symmetric Operator ◽  
Operator Spaces ◽  
Symmetric Operator Spaces

Weakly compact subsets of symmetric operator spaces

1991 ◽  
Vol 110 (1) ◽  
pp. 169-182 ◽  
Author(s):  
Peter G. Dodds ◽  
Theresa K. Dodds ◽  
Ben De Pagter
Keyword(s):  
Banach Space ◽  
Symmetric Operator ◽  
Von Neumann Algebra ◽  
Operator Spaces ◽  
Natural Conditions ◽  
Weakly Compact ◽  
Von Neumann ◽  
Finite Von Neumann Algebra ◽  
Measurable Operators ◽  
Symmetric Operator Spaces

AbstractUnder natural conditions it is shown that the rearrangement invariant hull of a weakly compact subset of a properly symmetric Banach space of measurable operators affiliated with a semi-finite von Neumann algebra is again relatively weakly compact.

scholarly journals The $p$-Banach Saks property in symmetric operator spaces

2007 ◽  
Vol 51 (4) ◽  
pp. 1207-1229 ◽  
Author(s):  
F. Lust-Piquard ◽  
F. Sukochev
Keyword(s):  
Symmetric Operator ◽  
Operator Spaces ◽  
Symmetric Operator Spaces

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

2008 ◽  
Vol 51 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Nigel Kalton ◽  
Fyodor Sukochev
Keyword(s):  
Symmetric Operator ◽  
Compact Operators ◽  
Operator Spaces ◽  
Marcinkiewicz Function ◽  
Symmetric Operator Spaces ◽  
Answering Questions

AbstractWe present a construction of singular rearrangement invariant functionals on Marcinkiewicz function/operator spaces. The functionals constructed differ from all previous examples in the literature in that they fail to be symmetric. In other words, the functional ϕ fails the condition that if (Hardy-Littlewood-Polya submajorization) and 0 ≤ x, y, then 0 ≤ ϕ(x) ≤ ϕ(y). We apply our results to singular traces on symmetric operator spaces (in particular on symmetrically-normed ideals of compact operators), answering questions raised by Guido and Isola.

scholarly journals COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES

2007 ◽  
Vol 50 (2) ◽  
pp. 293-324 ◽  
Author(s):  
Ben de Pagter ◽  
Fyodor Sukochev
Keyword(s):  
Symmetric Operator ◽  
Von Neumann Algebra ◽  
Adjoint Operator ◽  
Operator Spaces ◽  
Von Neumann ◽  
Finite Von Neumann Algebra ◽  
Operator Functions ◽  
Strongly Continuous Groups ◽  
Symmetric Operator Spaces ◽  
Groups Of Isometries

AbstractThe principal results in this paper are concerned with the description of domains of infinitesimal generators of strongly continuous groups of isometries in non-commutative operator spaces $E(\mathcal{M},\tau)$, which are induced by $\mathbb{R}$-flows on $\mathcal{M}$. In particular, we are concerned with the description of operator functions which leave the domain of such generators invariant in all symmetric operator spaces, associated with a semi-finite von Neumann algebra $\mathcal{M}$ and a separable function space $E$ on $(0,\infty)$. Furthermore, we apply our results to the study of operator functions for which $[D,x]\in E(\mathcal{M},\tau)$ implies that $[D,f(x)]\in E(\mathcal{M},\tau)$, where $D$ is an unbounded self-adjoint operator. Our methods are partly based on the recently developed theory of double operator integrals in symmetric operator spaces and the theory of adjoint $C_{0}$-semigroups.

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