Oxidation of Alcohols by [Cp*Rh(ppy)(OH)]+

Summary.  Rh(III) polypyridine complexes ([Cp ^*Rh(ppy)(H₂O)]²⁺; ppy = 2,2′-bipyridine, 2,2′-bipyridine-4,4′-dicarboxylate, o-phenanthroline, tetrahydro-4,4′-dialkyl-bis-oxazole) oxidize in organic or aqueous alkaline solution primary and secondary alcohols to aldehydes or ketones and are thereby reduced to the Rh(I) complexes Cp ^*Rh(ppy). The Rh(III) form can be regenerated byoxidants like pyruvate or oxygen, making the reaction quasi-catalytic. The reaction follows anautocatalytic pathway; hydrogen transfer from the α-CH₂ group of an alcoholate complex [Cp ^*Rh(ppy)(OR)]⁺ to Cp ^*Rh(I)(ppy) is suggested to yield the Rh(II) intermediate Cp ^*Rh(ppy)H as the key and rate determining step. The knowledge of Rh(III)/Rh(I) redox potentials allows to estimate the thermodynamic driving force of the reaction which is not more than about 300 mV.     

THE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORUSTHE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORU

1. IntroductionGiven a locally compact abelian group G and a multiplier p on G, one can associate tothem the twisted group C*-algebra C*(G, p), which is the universal object for unitary prepresentations of G. C* (Zm, p) is said to be a noncommutative torns of rank m and denotedby A.. The multiplier p determines a subgroup S. of G, called its symmetry group, andthe multiplier p is called totally skew if the symmetry group S. is trivial. And A. is calledcompletely irrational if p is totally…     

Representations of distributive semilattices in ideal lattices of various algebraic structures

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000.     

Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.     

Approximately unital operator systems

The main theme of this paper is to consider a notion of 'approximately unital operator systems' including both C*-algebras and unital operator systems.The goals are to prove a version of the Choi-Effros theorem for these systems,to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit,to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital ...     

The characterization of a class of quantum Markov semigroups and the associated operator-valued Dirichlet forms based on Hilbert <Emphasis Type="Italic">C</Emphasis>*-module <Emphasis Type="Italic">l</Emphasis><Subscript>2</Subscript>(<Emphasis Type="Italic">A</Emphasis>)

We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.     

拟绝对-*-κ-仿正规算子的谱性质

引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}.     

LENTICULAR NONCOMMUTATIVE TORI

All C*-algebras of sections of locally trivial C* -algebra bundles over ∏i=1sLki(ni) with fibres Aw Mc(C) are constructed, under the assumption that every completely irrational noncommutative torus Aw is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C*-algebra over whose cd-homogeneous C*-subalgebra restricted to the subspace Tr × T2 is realized as C(Tr) A1/d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lpcd is defined by twisting in by a totally skew multiplier p on Tr+2 × Zm-2. It is shown that is isomorphic to if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lpcd is not stablyisomorphic to if the cd-homogeneous C*-subalgebra of Lpcd restricted to some subspace LkiLki (ni) is realized as the crossed product by the obvious non-trivial action of Zki on a cd/ki-homogeneous C*-algebra over S2ni+1 for ki an integer greater than     

ON THE BOUNDEDNESS OF SPHERES IN F-SPACES

In this paper, some results concerning the relationship between the bounded-ness of some spheres and the local boundedness of the F*-space are presented. Moreover, some results about the compactness are also given.     

Stereoelectronic structure of MCl4-benzoyl chloride (M=Si,Ge, Sn) systems resulting from ab initio calculations and NQR 35Cl

Results of quantum-chemical calculations of MCl₄–C₆H₅COCl (M=Si, Ge, Sn) systems of 1?:?1 composition using RHF/3-21?G* and MP2/3-21?G* levels as well as those of 1?:?2 composition using the RHF/3-21?G* level have been represented. MCl₄?←?C₆H₅COCl complexes of 1?:?1 composition are energetically more advantageous. They are formed in solid state provided that the M···O distance in individual systems is considerably less than the sum of van der Waals radii of M and O and their total energies are appreciably less than the sum of total energies of components. These conditions are realized only for M=Sn. In systems of 1?:?2 compositions, calculated M···O distances are practically equal to the sum of covalent radii of M and O. Nonetheless, complexes with such composition are not formed in solid state. Total energy of the system which is lower than the sum of its components’ energies is not an indispensable condition for complex formation. The ³⁵Cl nuclear quadrupole resonance (NQR) frequencies and asymmetry parameters of the electric field gradient at the ³⁵Cl nuclei have been evaluated using the results of ab initio calculations.