共查询到20条相似文献,搜索用时 31 毫秒
1.
Jian-hua ZHANG~ Hong-ke DU Hui-xin CAO College of Mathematics Information Science Shaanxi Normal University Xi'an China 《中国科学A辑(英文版)》2007,(12)
In this paper,we introduce PropertyΠ_σof operator algebras and prove that nest sub- algebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have PropertyΠ_σ. Finally,we show that the tensor product formula alg_ML_1(?)alg_NL_2=alg_(M(?)N)(L_1(?)L_2) holds for any two finite-width CSLs L_1 and L_2 in arbitrary von Neumann algebras M and N,respectively. 相似文献
2.
《中国科学 数学(英文版)》2015,(8)
Let L be a type II1 factor with separable predual and τ be a normal faithful tracial state of L. We first show that the set of subfactors of L with property Γ, the set of type II1 subfactors of L with similarity property and the set of all Mc Duff subfactors of L are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite von Neumann algebra with a normal faithful trace,the set of all von Neumann subalgebras B of M such that B M is rigid is closed in the Hausdorff metric d2. 相似文献
3.
HOU ChengJun School of Mathematical Sciences Qufu Normal University Sh ong China 《中国科学A辑(英文版)》2008,(11)
Let L(FQ) ×α Z be the crossed product von Neumann algebra of the free group factor L(FQ), associated with the left regular representation λ of the free group FQ with the set {ur : r ∈ Q} of generators, by an automorphism α defined by α(λ(ur)) = exp(2πri)λ(ur), where Q is the rational number set. We show that L(FQ) ×α Z is a wΓ factor, and for each r ∈ Q, the von Neumann subalgebra Ar generated in L(FQ) ×α Z by λ(ur) and v is maximal injective, where v is the unitary implementing the automorphism α. In parti... 相似文献
4.
Dan LI 《数学学报(英文版)》2012,28(9):1845-1850
Extending the notion of property T of finite von Neumann algebras to general von Neumann algebras, we define and study in this paper property T** for (possibly non-unital) C* -algebras. We obtain several results of property T** parallel to those of property T for unital C* -algebras. Moreover, we show that a discrete group Γ has property T if and only if the group C* -algebra Cr* (Γ) (or equivalently, the reduced group C* -algebra Cr* (Γ)) has property T**. We also show that the compact operators K(l2 ) has property T** but c0 does not have property T**. 相似文献
5.
《数学物理学报(B辑英文版)》2015,(5)
Let(M, τ) be a noncommutative probability space,(Mn)n≥1a sequence of von Neumann subalgebras of M and N a von Neumann subalgebra of M. We introduce the notions ofμ-approach and orthogonal approach for(Mn)n≥1and prove that E(x|Mn)Lp--→E(x|N) for anyx∈Lp(M)(1 ≤p ∞) if and only if(Mn)n≥1 τ-approaches and orthogonally approaches N. 相似文献
6.
JinSong Wu 《中国科学 数学(英文版)》2012,55(5):977-984
A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes’s embedding property belong to just a few special classes (e.g.,amenable algebras and free group factors).In this article,we prove that von Neumann algebras satisfying Popa’s co-amenability have Connes’s embedding property. 相似文献
7.
For a vertex operator algebra V with conformal vector ω,we consider a class of vertex operator subalgebras and their conformal vectors.They are called semi-conformal vertex operator subalgebras and semiconformal vectors of(V,ω),respectively,and were used to study duality theory of vertex operator algebras via coset constructions.Using these objects attached to(V,ω),we shall understand the structure of the vertex operator algebra(V,ω).At first,we define the set Sc(V,ω)of semi-conformal vectors of V, then we prove that Sc(V,ω)is an affine algebraic variety with a partial ordering and an involution map.Corresponding to each semi-conformal vector,there is a unique maximal semi-conformal vertex operator subalgebra containing it.The properties of these subalgebras are invariants of vertex operator algebras.As an example,we describe the corresponding varieties of semi-conformal vectors for Heisenberg vertex operator algebras.As an application,we give two characterizations of Heisenberg vertex operator algebras using the properties of these varieties. 相似文献
8.
∞Ge(2003) asked the question whether LF∞ can be embedded into LF2 as a maximal subfactor.We answer it affirmatively with three different approaches, all containing the same key ingredient: the existence of maximal subgroups with infinite index. We also show that point stabilizer subgroups for every faithful, 4-transitive action on an infinite set give rise to maximal von Neumann subalgebras. By combining this with the known results on constructing faithful, highly transitive actions, we get many maximal von Neumann subalgebras arising from maximal subgroups with infinite index. 相似文献
9.
AntonioAIZPURU AntonioGUTIERREZ-DAVILA 《数学学报(英文版)》2004,20(5):949-960
In this paper we will study some familes and subalgebras F of P (N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A^xi, A ∈ F. As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces. 相似文献
10.
Wen Ming WU Li Guang WANG 《数学学报(英文版)》2007,23(3):491-496
11.
In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W*-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2A and the set of regular quadratic forms, where A is a finite and σ-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup {Tt }t∈R + L(l2A) is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L(l2A) is the von Neumann algebra of all adjointable module maps on l2A. 相似文献
12.
13.
Jian Lian CUI Department of Mathematical Sciences Tsinghua University Beijing P.R.China Department of Mathematics Shanxi Teachers University Linfen P.R.China Jin Chuan HOU Department of Mathematics Shanxi Teachers University Linfen P.R.China Department of Mathematics Shanxi University Taiyuan P.R.China 《应用数学学报(英文版)》2004,(4)
We show that every unital invertibility preserving linear map from a yon Neumann algebraonto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to aproblem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simplecomplex Banach algebra onto another,we also show that the following statements are equivalent:(1)Φ is an homomorphism;(2)Φ is completely invertibihty preserving;(3)Φ is 2-invertibility preserving. 相似文献
14.
In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras. 相似文献
15.
WU WenMing School of Mathematical Computer Science Chongqing Normal University Chongqing China 《中国科学A辑(英文版)》2008,(11)
Given the hyperbolic measure dxdy/y2 on the upper half plane H, the rational actions of PSL2(R) on H induces a continuous unitary representation α of this group on the Hilbert space L2(H, dxdy/y2). Supposing that A = {Mf : f ∈ L∞(H, dxdy/y2)}, we show that the crossed product R(A,α) is of type I. In fact, the crossed product R(A,α) is *-isomorphic to the von Neumann algebra B(L2(P,ν))■LK, where LK is the abelian group von Neumann algebra generated by the left regular representation of K. 相似文献
16.
We show that the reflexive algebra Alg(L) given by a double triangle lattice L in a finite factor M(with L" = M) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(L) ∩ Alg(L)~+.Our method can be used to prove similar results in finite-dimensional matrix algebras.As a consequence,we give a new proof to the main theorem by Hou and Zhang(2012). 相似文献
17.
A single-valued neutrosophic (SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to Lie algebras. We develop the concepts of SVN Lie subalgebras and SVN Lie ideals. We describe some interesting results of SVN Lie ideals. 相似文献
18.
An Extension of a Simply Inequality Between von Neumann–Jordan and James Constants in Banach Spaces 下载免费PDF全文
For a non-trivial Banach space X, let J(X), CNJ(X), C_(NJ)~(p)(X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C_(NJ)~(p)(X) ≤J(X) with p ≥ 2, which covers the well-known inequality CNJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al. 相似文献
19.
Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics^[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras. In this paper, we study solvable quadratic Lie algebras. In Section 1, we study quadratic solvable Lie algebras whose Cartan subalgebras consist of semi-simple elements. In Section 2,we present a procedure to construct a class of quadratic Lie algebras, and we can exhaust all solvable quadratic Lie algebras in such a way. All Lie algebras mentioned in this paper are finite dimensional Lie algebras over a field F of characteristic 0. 相似文献
20.
Maria BURGOS ;E Amin KAIDI ;Antonio Morales CAMPOY ;Antonio M. PERALTA ;Maribel RAMIREZ 《数学学报(英文版)》2008,24(2):185-200
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. 相似文献