共查询到20条相似文献,搜索用时 31 毫秒
1.
Uffe Haagerup 《Journal of Functional Analysis》1979,33(3):339-361
Let M be a von Neumann algebra, and N a sub von Neumann algebra of M. We prove that if φ and ψ are n.f.s. weights on N and M respectively, such that σtψ extends σtφ, then there is a unique n.f.s. operator valued weight T from M to N, such that ψ = φ ° T. Moreover we generalize the notion of modular automorphism groups associated with conditional expectations to operator valued weights. 相似文献
2.
A Connes 《Journal of Functional Analysis》1975,18(3):318-327
A factor M is the cross product of an abelian von Neumann algebra by a single automorphism iff there exists an increasing sequence of normal conditional expectations of M onto finite-dimensional subalgebras Nk with (U Nk)? = M. Assuming the uniqueness of the hyperfinite factor of type II∞, we prove then that any hyperfinite factor of type III0 is the cross product of an abelian von Neumann algebra by a single automorphism. 相似文献
3.
If (N,t) ({\cal N},\tau) is a finite von Neumann algebra and if (M,n) ({\cal M},\nu) is an infinite von Neumann algebra, then Lp(M,n) L_{p}({\cal M},\nu) does not Banach embed in Lp(N,t) L_{p}({\cal N},\tau) for all p ? (0,1) p\in (0,1) . We also characterize subspaces of $ L_{p}({\cal N},\tau),\ 0< p <1 $ L_{p}({\cal N},\tau),\ 0< p <1 containing a copy of lp. 相似文献
4.
This paper is devoted to derivations on the algebra S 0(M, τ) of all τ-compact operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. The main result asserts that every t τ -continuous derivation ${D : S_0(M, \tau) \rightarrow S_{0}(M, \tau)}$ is spatial and implemented by a τ-measurable operator affiliated with M, where t τ denotes the measure topology on S 0(M, τ). We also show the automatic t τ -continuity of all derivations on S 0(M, τ) for properly infinite von Neumann algebras M. Thus in the properly infinite case the condition of t τ -continuity of the derivation is redundant for its spatiality. 相似文献
5.
In this paper we set up a representation theorem for tracial gauge norms on finite von Neumann algebras satisfying the weak Dixmier property in terms of Ky Fan norms. Examples of tracial gauge norms on finite von Neumann algebras satisfying the weak Dixmier property include unitarily invariant norms on finite factors (type II1 factors and Mn(C)) and symmetric gauge norms on L∞[0,1] and Cn. As the first application, we obtain that the class of unitarily invariant norms on a type II1 factor coincides with the class of symmetric gauge norms on L∞[0,1] and von Neumann's classical result [J. von Neumann, Some matrix-inequalities and metrization of matrix-space, Tomsk. Univ. Rev. 1 (1937) 286-300] on unitarily invariant norms on Mn(C). As the second application, Ky Fan's dominance theorem [Ky Fan, Maximum properties and inequalities for the eigenvalues of completely continuous operators, Proc. Natl. Acad. Sci. USA 37 (1951) 760-766] is obtained for finite von Neumann algebras satisfying the weak Dixmier property. As the third application, some classical results in non-commutative Lp-theory (e.g., non-commutative Hölder's inequality, duality and reflexivity of non-commutative Lp-spaces) are obtained for general unitarily invariant norms on finite factors. We also investigate the extreme points of N(M), the convex compact set (in the pointwise weak topology) of normalized unitarily invariant norms (the norm of the identity operator is 1) on a finite factor M. We obtain all extreme points of N(M2(C)) and some extreme points of N(Mn(C)) (n?3). For a type II1 factor M, we prove that if t (0?t?1) is a rational number then the Ky Fan tth norm is an extreme point of N(M). 相似文献
6.
We generalise the local index formula of Connes and Moscovici to the case of spectral triples for a *-subalgebra A of a general semifinite von Neumann algebra. In this setting it gives a formula for spectral flow along a path joining an unbounded self-adjoint Breuer-Fredholm operator, affiliated to the von Neumann algebra, to a unitarily equivalent operator. Our proof is novel even in the setting of the original theorem and relies on the introduction of a function valued cocycle which is ‘almost’ a (b,B)-cocycle in the cyclic cohomology of A. 相似文献
7.
Palle E.T. Jorgensen 《Journal of Functional Analysis》1979,34(1):138-145
We prove a commutation theorem for point ultraweakly continuous oneparameter groups of automorphisms of von Neumann algebras. If αt, is such a group in Aut() for a von Neumann algebra , we show the equivalence of the following three conditions on an ultraweakly continuous linear transformation μ: → : (a) μ commutes weakly with the infinitesimal generator for αt; (b) μ ° αt = αt ° μ, t ∈ R; and (c) μ leaves invariant each of the spectral subspaces associated with αt. A simple condition which is applicable when μ is an automorphism is pointed out. 相似文献
8.
Domingo A. Herrero 《Integral Equations and Operator Theory》1983,6(1):515-524
Let T be an injective bilateral weighted shift onl 2 thought as "multiplication by λ" on a space of formal Laurent series L2(β). (a) If L2(β) is contained in a space of quasi-analytic class of functions, then the point spectrum σp(T?) of T? contains a circle and the cyclic invariant subspaceM f of T generated by f is simply invariant (i.e., ∩{(Tk M f)?: k ≥ 0}= {0}) for each f in L2(β); (b) If L2(β) contains a non-quasi-analytic class of functions (defined on a circle г) of a certain type related with the weight sequence of T, then there exists f in L2(ß) such thatM f is a non-trivial doubly invariant subspace (i.e., (TM f)? =M f); furthermore, if г ? σp(T*), then σp (T*) = г and f can be chosen so that σp([T∣M f]*) = г?{α}, for some α ε г. Several examples show that the gap between operators satisfying (a) and operators satisfying (b) is rather small. 相似文献
9.
Baruch Solel 《Journal of Functional Analysis》2006,235(2):593-618
We prove that every pair of commuting CP maps on a von Neumann algebra M can be dilated to a commuting pair of endomorphisms (on a larger von Neumann algebra). To achieve this, we first prove that every completely contractive representation of a product system of C∗-correspondences over the semigroup N2 can be dilated to an isometric (or Toeplitz) representation. 相似文献
10.
A. Connes 《Journal of Functional Analysis》1980,35(2):153-164
If M is a von Neumann algebra in , each faithful weight ψ on M′ defines an operator-valued weight ψ?1 of on M. For each weight ? on M the positive unbounded operator satisfies all the usual properties of a Radon-Nikodym derivative. 相似文献
11.
J.K. Verma 《代数通讯》2013,41(12):2999-3024
Let (R,m) be a local ring. Let SM denote the Rees algebra S=R[mrt] localized at its unique maximal homogeneous ideal M=(m,mrt). Let TN denote the extended Rees algebra T= R[mrt, t-1] localized at its unique maximal homogeneous idea N= (t?1,m,mr). Multiplicity formulas are developedfor SM and TN. These are used to find necessaIy and sufficient conditions on a Cohen-Macaulay local ring (R,m) and r so that SM and TN are Cohen-Macaulay with minimal multiplicity 相似文献
12.
A Van Daele 《Journal of Functional Analysis》1974,15(4):378-393
Let M be a von Neumann algebra with separating and cyclic vector ξ0. The map with x?M has a least closed extension S. Tomita proved that the isometric involution J and the positive self-adjoint operator Δ obtained from the polar decomposition of S satisfy JMJ = M′ and ΔitMΔ?it = M for any real t. More generally, he obtained similar results for the left von Neumann algebra of any generalized Hilbert algebra. In this paper a shorter proof of his results is given. 相似文献
13.
We show that if A is a Hilbert–space operator, then the set of all projections onto hyperinvariant subspaces of A, which is contained in the von Neumann algebra υN(A) that is generated by A, is independent of the representation of υ N(A), thought of as an abstract W*–algebra. We modify a technique of Foias, Ko, Jung and Pearcy to get a method for finding nontrivial hyperinvariant subspaces
of certain operators in finite von Neumann algebras. We introduce the B–circular operators as a special case of Speicher's B–Gaussian operators in free probability theory, and we prove several results about a B–circular operator z, including formulas for the B–valued Cauchy– and R–transforms of z*z. We show that a large class of L∞([0,1])–circular operators in finite von Neumann algebras have nontrivial hyperinvariant subspaces, and that another large
class of them can be embedded in the free group factor L(F3). These results generalize some of what is known about the quasinilpotent DT–operator.
Supported in part by NSF Grant DMS-0300336.
with an Appendix by Gabriel Tucci 相似文献
14.
Let M\mathcal{M} and N\mathcal{N} be the von Neumann algebras induced by the rational action of the group SL
2(ℝ) and its subgroup P on the upper half plane
\mathbbH\mathbb{H}. We have shown that N\mathcal{N} is spatial isomorphic to the group von Neumann algebra LP\mathcal{L}_P and characterized M\mathcal{M} and its commutant M¢\mathcal{M}' and gotten a generalization of the Mautner’s lemma. It is also shown that the Berezin operator commutates with the Laplacian
operator. 相似文献
15.
Herbert Halpern 《Journal of Functional Analysis》1980,36(3):313-342
Let be a von Neumann algebra, let σ be a strongly continuous representation of the locally compact abelian group G as 1-automorphisms of . Let M(σ) be the Banach algebra of bounded linear operators on generated by ∝ σtdμ(t) (μ?M(G)). Then it is shown that M(σ) is semisimple whenever either (i) has a σ-invariant faithful, normal, semifinite, weight (ii) σ is an inner representation or (iii) G is discrete and each σt is inner. It is shown that the Banach algebra L(σ) generated by is semisimple if a is an integrable representation. Furthermore, if σ is an inner representation with compact spectrum, it is shown that L(σ) is embedded in a commutative, semisimple, regular Banach algebra with isometric involution that is generated by projections. This algebra is contained in the ultraweakly continuous linear operators on . Also the spectral subspaces of σ are given in terms of projections. 相似文献
16.
Turdebek N. Bekjan 《Journal of Functional Analysis》2008,254(9):2401-2418
Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L2(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations. 相似文献
17.
J.K. BrooksKazuyuki Saitô J.D.Maitland Wright 《Journal of Mathematical Analysis and Applications》2002,276(1):160-167
Let (φn) be a norm bounded sequence in the pre-dual of a von Neumann algebra M. In general it is not true that this sequence has a weakly convergent subsequence. But given a normal state ψ, then, for any ε>0, there exists a projection e such that ψ(1−e)?ε and the restriction of (φn) to eMe has a subsequence which converges weakly to a normal functional on eMe. 相似文献
18.
Shavkat A. Ayupov Karimbergen K. Kudaybergenov Rauaj T. Djumamuratov 《Central European Journal of Mathematics》2012,10(2):656-664
Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t
c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t
c(M) restricted to the set E(M)
h
of self-adjoint elements of E(M) coincides with the order topology on E(M)
h
if and only if M is a σ-finite type Ifin von Neumann algebra. 相似文献
19.
20.
M. Junge 《Geometric And Functional Analysis》2000,10(2):389-406
It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomorphic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative Lp(N, t) L_p(N, \tau) -spaces defined by a finite trace on a finite von Neumann algebra. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting. 相似文献