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Search: All articles in the CJM digital archive with keyword trace formula

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1. CJM Online first

Hua, Jiajie; Lin, Huaxin
 Rotation algebras and the Exel trace formula We found that if $u$ and $v$ are any two unitaries in a unital $C^*$-algebra with $\|uv-vu\|\lt 2$ and $uvu^*v^*$ commutes with $u$ and $v,$ then the $C^*$-subalgebra $A_{u,v}$ generated by $u$ and $v$ is isomorphic to a quotient of some rotation algebra $A_\theta$ provided that $A_{u,v}$ has a unique tracial state. We also found that the Exel trace formula holds in any unital $C^*$-algebra. Let $\theta\in (-1/2, 1/2)$ be a real number. We prove the following: For any $\epsilon\gt 0,$ there exists $\delta\gt 0$ satisfying the following: if $u$ and $v$ are two unitaries in any unital simple $C^*$-algebra $A$ with tracial rank zero such that $\|uv-e^{2\pi i\theta}vu\|\lt \delta \text{ and } {1\over{2\pi i}}\tau(\log(uvu^*v^*))=\theta,$ for all tracial state $\tau$ of $A,$ then there exists a pair of unitaries $\tilde{u}$ and $\tilde{v}$ in $A$ such that $\tilde{u}\tilde{v}=e^{2\pi i\theta} \tilde{v}\tilde{u},\,\, \|u-\tilde{u}\|\lt \epsilon \text{ and } \|v-\tilde{v}\|\lt \epsilon.$ Keywords:rotation algebras, Exel trace formulaCategory:46L05

2. CJM 2012 (vol 64 pp. 497)

Li, Wen-Wei
 Le lemme fondamental pondÃ©rÃ© pour le groupe mÃ©taplectique Dans cet article, on Ã©nonce une variante du lemme fondamental pondÃ©rÃ© d'Arthur pour le groupe mÃ©taplectique de Weil, qui sera un ingrÃ©dient indispensable de la stabilisation de la formule des traces. Pour un corps de caractÃ©ristique rÃ©siduelle suffisamment grande, on en donne une dÃ©monstration Ã  l'aide de la mÃ©thode de descente, qui est conditionnelle: on admet le lemme fondamental pondÃ©rÃ© non standard sur les algÃ¨bres de Lie. Vu les travaux de Chaudouard et Laumon, on s'attend Ã  ce que cette condition soit ultÃ©rieurement vÃ©rifiÃ©e. Keywords:fundamental lemma, metaplectic group, endoscopy, trace formulaCategories:11F70, 11F27, 22E50

3. CJM 2009 (vol 62 pp. 133)

Makarov, Konstantin A.; Skripka, Anna
 Some Applications of the Perturbation Determinant in Finite von Neumann Algebras In the finite von Neumann algebra setting, we introduce the concept of a perturbation determinant associated with a pair of self-adjoint elements $H_0$ and $H$ in the algebra and relate it to the concept of the de la Harpe--Skandalis homotopy invariant determinant associated with piecewise $C^1$-paths of operators joining $H_0$ and $H$. We obtain an analog of Krein's formula that relates the perturbation determinant and the spectral shift function and, based on this relation, we derive subsequently (i) the Birman--Solomyak formula for a general non-linear perturbation, (ii) a universality of a spectral averaging, and (iii) a generalization of the Dixmier--Fuglede--Kadison differentiation formula. Keywords:perturbation determinant, trace formulae, von Neumann algebrasCategories:47A55, 47C15, 47A53

4. CJM 1999 (vol 51 pp. 952)

Deitmar, Anton; Hoffmann, Werner
 On Limit Multiplicities for Spaces of Automorphic Forms Let $\Gamma$ be a rank-one arithmetic subgroup of a semisimple Lie group~$G$. For fixed $K$-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of~$G$, whose discrete part encodes the dimensions of the spaces of square-integrable $\Gamma$-automorphic forms. It is shown that this distribution converges to the Plancherel measure of $G$ when $\Ga$ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices $\Gamma$ follows from results of DeGeorge-Wallach and Delorme. Keywords:limit multiplicities, automorphic forms, noncompact quotients, Selberg trace formula, functional calculusCategories:11F72, 22E30, 22E40, 43A85, 58G25