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1.
We define two canonical cohomology theories for Hopf C*-algebrasand for Hopf von Neumann algebras (with coefficients in theircomodules). We then study the situations when these cohomologiesvanish. The cases of locally compact groups and compact quantumgroups are considered in more detail. E-mail: c.k.ng{at}qub.ac.uk2000 Mathematical Subject Classification: primary 46L05, 46L55;secondary 43A07, 22D25. 相似文献
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A commutative fusion algebra is proved to be amenable if and only if the associated regular representation is bounded. 相似文献
3.
R. I. Grigorchuk 《Mathematical Notes》1996,60(3):274-282
The paper is devoted to the study of weights on groups. A connection between weight functions and harmonic functions is established.
A relationship between the weight theory on groups with the “Tychonoff property” and the theory of bounded cohomology is presented.
It is proved that the Beurling algebraℓ1 (G, ω) constructed for the weightω is amenable if and only if the groupG is amenable and the weightω is equivalent to a multiplicative characterχ:G→ℝ+.
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 448–460, September, 1996.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00974 and by the
INTAS Foundation under grant No. 94-3420. 相似文献
4.
Let X be a compact Hausdorff space and A a Banach algebra. We investigate amenability properties of the algebra C(X,A) of all A -valued continuous functions. We show that C(X,A) has a bounded approximate diagonal if and only if A has a bounded approximate diagonal; if A has a compactly central approximate diagonal (unbounded) then C(X,A) has a compactly approximate diagonal. Weak amenability of C(X,A) for commutative A is also considered. 相似文献
5.
Yuji Takahashi 《Proceedings of the American Mathematical Society》1996,124(1):193-196
It is shown that Paschke's result cannot be generalized to the [IN]-group setting given by Lau and Paterson. This resolves negatively a problem raised by Lau and Paterson.
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Marie Choda 《Proceedings of the American Mathematical Society》2006,134(10):2905-2911
Let be the automorphism of the free group which is arising from a permutation of the free generators of The naturally induces the automorphism of the reduced -algebra and also the automorphism of the group factor We show that the Brown-Germain entropy is zero. This implies that the Brown-Voiculescu topological entropy the Connes-Narnhofer-Thirring dynamical entropy and the Connes-Størmer entropy are all zero.
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A. G. Myasnikov 《Mathematical Notes》1999,66(6):726-732
Weak versions of amenability components of BanachL
1(G)-modules are considered. Using these versions, a mean ergodic theorem for locally compact groups is formulated. The possibility
of using weak amenability components of operatorL
1(G)-modules to characterize ameable groups is studied.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 879–886, December, 1999. 相似文献
9.
In the present paper we introduce a new definition for the Fourier space A (K) of a locally compact Hausdorff hypergroup K and prove that it is a Banach subspace of B (K). This definition coincides with that of Amini and Medghalchi in the case where K is a tensor hypergroup, and also with that of Vrem which is given only for compact hypergroups. We prove that Ap (K)* = PMq (K), where q is the exponent conjugate to p, in particular A (K)* = VN (K). Also we show that for Pontryagin hypergroups, A (K) = L2(K) * L2(K) = F (L1( )), where F stands for the Fourier transform on . Furthermore there is an equivalent norm on A (K) which makes A (K) into a Banach algebra isomorphic with L1( ). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
10.
Peter J. Wood 《Proceedings of the American Mathematical Society》2000,128(2):445-451
In this paper we provide a necessary condition for a closed ideal in the Fourier algebra of a locally compact amenable group to be completely complemented. The classification of completely complemented ideals is completed in the case of an amenable discrete group. We also investigate the ideals possessing a bounded approximate identity.