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We study property (T) and the fixed-point property for actions on L
p
and other Banach spaces. We show that property (T) holds when L
2 is replaced by L
p
(and even a subspace/quotient of L
p
), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L
p
follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L
p
holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices
in products of general groups on superreflexive spaces.
Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander
partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US). 相似文献
3.
Laura Bader Nicola Durante Maska Law Guglielmo Lunardon Tim Penttila 《Designs, Codes and Cryptography》2003,29(1-3):41-50
We do the tentative beginnings of a study of BLT-sets of generalised quadrangles via their symmetries. In particular, the study of whorls about a line leads us to hyperbolic reflections preserving a BLT-set of Q(4, q). 相似文献
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Richard Frederick William Bader Paul Lode Albert Popelier Todd Alan Keith 《Angewandte Chemie (International ed. in English)》1994,33(6):620-631
It is the purpose of this review to demonstrate that the empirical classification of the observations of chemistry in terms of the properties assigned to functional groups is a consequence of and is predicted by physics. This is accomplished by showing that the atoms and functional groups of chemistry can be identified with bounded space-filling objects whose properties are defined by quantum mechanics. The quantum mechanical definition of a group is combined with a new pictorial representation of its form to obtain a unified picture which should make it eminently recognizable to chemists. This picture, when combined with the demonstrated ability of these groups to recover the measured properties of atoms in molecules, is offered as one which meets the expectations a chemist associates with the concept of a functional group. The manner in which this physical definition of a group differs fundamentally from models of functional groups based upon molecular orbital theory is discussed. 相似文献
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Helmut Simon Johann Bader Helmut Günther Stefan Neumann Jordanes Thanos 《Angewandte Chemie (International ed. in English)》1985,24(7):539-553
It has been known for many decades that chiral compounds can be obtained by stereospecific biocatalytic reduction. Further significant methodological developments in this field have, however, only been made during the past ten years; they include the application of previously unused microorganisms and electron donors, the discovery of additional substrates for the known reductases, the development of methods for regenerating reduced pyridine nucleotides, and the discovery of new reductases which were sought for specific preparative purposes. Many chiral compounds can now be synthesized by microbial hydrogenation using H2 and hydrogenase-containing microorganisms as well as by electromicrobial or electroenzymatic reduction. In the two latter methods, anaerobic or aerobic organisms are supplied with electrons from electrochemically reduced, artificial mediators, e.g., methyl viologen. Reductases that do not require pyridine nucleotides and can accept electrons directly from reduced viologens are especially useful. Two examples of this type of enzyme are described which are of preparative interest. Many cells contain methyl viologen-dependent NAD(P) reductases, a large number of which have still not been characterized. A productivity number is proposed which allows different methods of bioconversion with microorganisms to be compared. The productivity numbers of compounds synthesized by the methods described in this review are often 10- to 100-fold higher than those of substances obtained by conventional techniques. 相似文献