Commutator structure of operator ideals

Dykema, Ken; Figiel, T.; Weiss, Gary; Wodzicki, Mariusz

doi:10.1016/s0001-8708(03)00141-5

Cited by 97 publications

(159 citation statements)

References 45 publications

Supporting

Mentioning

154

Contrasting

Unclassified

Order By: Relevance

“…For p > 1, the ideal L p,∞ does not admit a non-zero trace while for p = 1, there exists a plethora of traces on L 1,∞ (see e.g. [9] or [14]). An example of a trace on L 1,∞ is the restriction (from M 1,∞ ) of the Dixmier trace introduced in [8] that we now explain.…”

Section: 3mentioning

confidence: 99%

See 1 more Smart Citation

Universal measurability and the Hochschild class of the Chern character

Carey¹,

Rennie²,

Sukochev³

et al. 2016

J. Spectr. Theory

View full text Add to dashboard Cite

Abstract. We study notions of measurability for singular traces, and characterise universal measurability for operators in Dixmier ideals. This measurability result is then applied to improve on the various proofs of Connes' identification of the Hochschild class of the Chern character of Dixmier summable spectral triples.The measurability results show that the identification of the Hochschild class is independent of the choice of singular trace. As a corollary we obtain strong information on the asymptotics of the eigenvalues of operators naturally associated to spectral triples (A, H, D) and Hochschild cycles for A.

show abstract

Section: 3mentioning

confidence: 99%

“…We consider auxiliary multilinear mappings which generalise the mappings W m , 1 ≤ m ≤ p, introduced above in Equation (9). For A ⊂ {1, .…”

Section: Proofsmentioning

confidence: 99%

Universal measurability and the Hochschild class of the Chern character

Carey¹,

Rennie²,

Sukochev³

et al. 2016

J. Spectr. Theory

View full text Add to dashboard Cite

show abstract

“…For later use, we now recall a few facts concerning Banach ideals of operators on the complex Hilbert space H (see [15] and also [13]). For all T ∈ B(H) denote…”

Section: Symplectic Leaves In Preduals Of Operator Idealsmentioning

confidence: 99%

“…On the topological level, this corresponds to the fact that any two symmetric norming functions define the same topology (in fact, the norm topology) on any unitary orbit of a finite-rank operator, as a consequence of Lemma 4.3. We should point out that there exist a large variety of symmetric norming functions, defining various types of operator ideals like Schatten, Lorentz, Orlicz and so on (see [13] for a survey of this subject). By way of illustrating this remark, we recall that we have already mentioned in Remark 4.2(iii) the functions Φ p (·) = · ℓ p that define the Schatten ideals.…”

Section: Notation 54mentioning

confidence: 99%

Symplectic leaves in real banach Lie–Poisson spaces

Beltiţă

Raţiu

2005

GAFA, Geom. funct. anal.

View full text Add to dashboard Cite

We present several large classes of real Banach Lie-Poisson spaces whose characteristic distributions are integrable, the integral manifolds being symplectic leaves just as in finite dimensions. We also investigate when these leaves are embedded submanifolds or when they have Kähler structures. Our results apply to the real Banach Lie-Poisson spaces provided by the self-adjoint parts of preduals of arbitrary W * -algebras, as well as of certain operator ideals.

show abstract

“…For p > 1, the ideal L p,∞ does not admit a non-zero trace while for p = 1, there exists a plethora of traces on L 1,∞ (see e.g. [18] or [25]). An example of a trace on L 1,∞ is the Dixmier trace introduced in [15] that we now explain.…”

Section: 3mentioning

confidence: 99%