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1. CJM 2011 (vol 63 pp. 798)

Daws, Matthew
 Representing Multipliers of the Fourier Algebra on Non-Commutative \$L^p\$ Spaces We show that the multiplier algebra of the Fourier algebra on a locally compact group \$G\$ can be isometrically represented on a direct sum on non-commutative \$L^p\$ spaces associated with the right von Neumann algebra of \$G\$. The resulting image is the idealiser of the image of the Fourier algebra. If these spaces are given their canonical operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative \$L^p\$ spaces we construct and show that they are completely isometric to those considered recently by Forrest, Lee, and Samei. We improve a result of theirs about module homomorphisms. We suggest a definition of a Figa-Talamanca-Herz algebra built out of these non-commutative \$L^p\$ spaces, say \$A_p(\widehat G)\$. It is shown that \$A_2(\widehat G)\$ is isometric to \$L^1(G)\$, generalising the abelian situation. Keywords:multiplier, Fourier algebra, non-commutative \$L^p\$ space, complex interpolationCategories:43A22, 43A30, 46L51, 22D25, 42B15, 46L07, 46L52

2. CJM 2009 (vol 61 pp. 241)

Azamov, N. A.; Carey, A. L.; Dodds, P. G.; Sukochev, F. A.
 Operator Integrals, Spectral Shift, and Spectral Flow We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general \vNa s. For semifinite \vNa s we give applications to the Fr\'echet differentiation of operator functions that sharpen existing results, and establish the Birman--Solomyak representation of the spectral shift function of M.\,G.\,Krein in terms of an average of spectral measures in the type II setting. We also exhibit a surprising connection between the spectral shift function and spectral flow. Categories:47A56, 47B49, 47A55, 46L51