Double Operator Integrals
By B. Pagter, H. Witvliet, Fedor Sukochev. 2002
80 citations recorded by the source corpus.
Subfields: Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a3ee6db1afa9739e0bc01e2bc20b7a6762a6ced9
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In Mathematical Physics
Citations in the corpus
- Operator-Lipschitz functions in Schatten–von Neumann classes (2009, background): “dFµ ∈ M, λ,µ ∈ R. Recall that if x,y ∈ L2, then the mapping (λ,µ) 7→dνx,y(λ,µ) := τ ydEλxdFµ , λ,µ ∈ R is a complex-valued σ-additive measure on R2 with total variation not exceeding kxk 2 kyk 2 (see [4]). If now φ : R2 7→C is a bounded Borel function, then the latter implies that (x,y) 7→ Z R2 φ(λ,”
- Double Operator Integrals in a Hilbert Space (2003, background): “As it was already mentioned in the Introduction, recently a new interest in operator integrals arose on another technical basis, see [ 29 ], [28] and references therein.”
- Operator Integrals, Spectral Shift, and Spectral Flow (2007, methodology): “Our approach is conceptually simpler than those of [29, 30 ], although it applies to a somewhat narrower class of functions.”
- Smooth Fourier multipliers on group von Neumann algebras (2010, methodology): “f(x) −f(y) x−y dµ(x)adν(y) have been intensively studied in the literature, following Birman/Solomyak we find results from de Pagter/Sukochev and the impressive recent work of Peller, see for instance [2, 3, 8, 23, 24] and the references therein. Of course, we may understand this theory as a continuo”
- Spectral shift function of higher order (2009, background): “n. Remark 3.4. In the special case n =1, the multilinear operator Tφ becomes a linear operator on Lα. For a large class of functions φ, the operator Tφ coincides with the double operator integral Tˆφ [21] (see below and also see referencescited in [6,21]). In particular, it is known that on the Hilb”