共查询到20条相似文献,搜索用时 0 毫秒
1.
Justin Peters 《Journal of Functional Analysis》1984,59(3):498-534
Given a C1-algebra and endomorphim α, there is an associated nonselfadjoint operator algebra + Xα, called the semi-crossed product of with α. If α is an automorphim, + Xα can be identified with a subalgebra of the C1-crossed product + Xα. If is commutative and α is an automorphim satisfying certain conditions, + Xα is an operator algebra of the type studied by Arveson and Josephson. Suppose S is a locally compact Hausdorff space, φ: S → S is a continuous and proper map, and α is the endomorphim of U=C0(S) given by α(?) = ? ō φ. Necessary and sufficient conditions on the map φ are given to insure that the semi-crossed product Z+XαC0(S) is (i) semiprime; (ii) semisimple; (ii) strongly semisimple. 相似文献
2.
Simon Wassermann 《Journal of Functional Analysis》1976,23(3):239-254
If A and B are C1-algebras there is, in general, a multiplicity of C1-norms on their algebraic tensor product A ⊙ B, including maximal and minimal norms ν and α, respectively. A is said to be nuclear if α and ν coincide, for arbitrary B. The earliest example, due to Takesaki [11], of a nonnuclear C1-algebra was , the C1-algebra generated by the left regular representation of the free group on two generators F2. It is shown here that W1-algebras, with the exception of certain finite type I's, are nonnuclear.If is the group C1-algebra of F2, there is a canonical homomorphism λl of onto . The principal result of this paper is that there is a norm ζ on , distinct from α, relative to which the homomorphism is bounded ( being endowed with the norm α). Thus quotients do not, in general, respect the norm α; a consequence of this is that the set of ideals of the α-tensor product of C1-algebras A and B may properly contain the set of product ideals {}.Let A and B be C1-algebras. If A or B is a W1-algebra there are on A ⊙ B certain C1-norms, defined recently by Effros and Lance [3], the definitions of which take account of normality. In the final section of the paper it is shown by example that these norms, with α and ν, can be mutually distinct. 相似文献
3.
F.Javier Thayer 《Journal of Functional Analysis》1977,25(1):50-57
We consider perturbations of C1-algebras by compact operators. We show that if A is a separable liminal algebra of operators on a separable Hilbert space, then it is a subalgebra of a compact perturbation of a block diagonal algebra. 相似文献
4.
A forest is a finite partially ordered set F such that for x, y, z?F with x ? z, y ? z one has x ? y or y ? x. In this paper we give a complete characterization of all separable C1-algebras with a finite dual , for which Prim is a forest with inclusion as partial order. These results are extended to certain separable C1-algebras with a countable dual. As an example these results are used to characterize completely all separable C1-algebras with a three point dual. 相似文献
5.
The question of which C1-algebras have only inner derivations has been considered by a number of authors for 25 years. The separable case is completely solved, so this paper deals only with the non-separable case. In particular, we show that the C1-tensor product of a von Neumann algebra and an abelian C1-algebra has only inner derivations. Other special types of C1-algebras are shown to have only inner derivations as well such as the C1-tensor product of L(H) (all bounded operators on separable Hilbert space) and any separable C1-algebra having only inner derivations. Derivations from a smaller C1-algebra into a larger one are also considered, and this concept is generalized to include derivations between C1-algebras connected by a 1-homomorphism. Finally, we consider the general problem of a sequence of linear functionals on a C1-algebra which converges to zero (in norm) when restricted to any abelian C1-subalgebra. Does such a sequence converge to zero in norm? The answer is “yes” for normal functionals on L(H), but unknown in general. 相似文献
6.
Bruce E Blackadar 《Journal of Functional Analysis》1980,38(2):156-168
The relations between the set of traces on a simple approximately finite dimensional C1-algebra A and the algebraic and geometric properties of the Elliott dimension group K0(A) are studied. It is shown that every metrizable Choquet simplex occurs as the set of normalized traces of a simple unital AF algebra. A simple AF algebra can have both finite and infinite traces, so a finite simple AF algebra need not be algebraically simple. It is shown that a simple AF algebra is algebraically simple if and only if it has no infinite traces, and is stable if and only if it has no finite traces. 相似文献
7.
Jan Søreng 《Journal of Functional Analysis》1976,22(4):390-404
Pure states of simple C1-algebras with identity are studied. We prove that pure states of such algebras have a product decomposition property, and that two pure states are unitarily equivalent if and only if they are asymptotically equal. 相似文献
8.
R.R Smith 《Journal of Functional Analysis》1985,64(3):330-337
It is shown that a C1-algebra is nuclear if and only if the identity map can be approximated in the point norm topology by complete contractions factoring through matrix algebras. 相似文献
9.
Alan McIntosh 《Journal of Functional Analysis》1978,30(2):264-275
It is shown that there is a closed symmetric derivation δ of a C1-algebra with dense domain (δ), an element A = A1 ?(δ), and a C1-function such that (A)?(δ). Some estimates are derived for , where 0 < α < 1. It is shown that there exists a family of one-one self-adjoint operators S(t) in (H) which depends linearly on t, while is not differentiable. It is also shown that there exists (H) which is not C1-self-adjoint even though it satisfies for all t ? 相似文献
10.
We introduce an equivalence relation among the positive elements in a C1 and show that the algebra is (semi-) finite if and only if there is a separating family of (semi-) finite traces. Concentrating on simple, semi-finite C1-algebras we relate geometrical properties in the cone of equivalence classes to functional analytic properties of the algebra, such as the number of normalized traces and their possible values on a given element. The paper may be considered as an attempt to extend Murray and von Neumann's type and equivalence theory to C1-algebras. 相似文献
11.
12.
Geoffrey Price 《Journal of Functional Analysis》1982,49(2):145-151
Let be a UHF-algebra of Glimm type n∞, and {αg: g?G} a strongly continuous group of 1-automorphisms of product type on , for G compact. Let α be the C1-subalgebra of fixed elements of . We show that any extremal normalized trace on α arises as the restriction of a symmetric product state ? on of the form ? = ?k?1 ω. As an example we classify the extremal traces on α for the case G = SU(n), αg = ?k ? 1 Ad(g). 相似文献
13.
14.
15.
Dana P Williams 《Journal of Functional Analysis》1981,41(1):40-76
We obtain several results characterizing when transformation group C1-algebras have continuous trace. These results can be stated most succinctly when () is second countable, and the stability groups are contained in a fixed abelian subgroup. In this case, has continuous trace if and only if the stability groups vary continuously on Ω and compact subsets of Ω are wandering in an appropriate sense. In general, we must assume that the stability groups vary continuously, and if () is not second countable, that the natural maps of onto G · x are homeomorphisms for each x. Then has continuous trace if and only if compact subsets of Ω are wandering and an additional C1-algebra, constructed from the stability groups and Ω, has continuous trace. 相似文献
16.
17.
Helge Elbrønd Jensen 《Journal of Functional Analysis》1983,50(2):127-132
The paper gives a complete classification of all separable C1-algebras with countable spectrum, for which each point in the spectrum has a finite neighbourhood. 相似文献
18.
George A Elliott 《Journal of Functional Analysis》1974,17(4):395-408
It is shown that if A is the C1-algebra inductive limit of a sequence of finite-dimensional C1-algebras, then for each closed two-sided ideal J of A derivations can be lifted to A from , and for each projection e in A derivations can be extended to A from eAe. An application of the second result is given. 相似文献
19.
Roberto Longo 《Journal of Functional Analysis》1979,34(1):21-28
We show that a derivation of a C1-algebra is automatically relative bounded with respect to any closed 1derivation of with smaller domain. We give also some related results on the automatic continuity of derivations in certain Banach algebras. 相似文献
20.
Maria Fragoulopoulou 《Journal of Mathematical Analysis and Applications》1985,108(2):422-429
The classical transitivity theorem of R. Kadison for C1-algebras is here extended to the case of a locally C1-algebra E. As a consequence, within the same context, various standard facts referred to the space of representations of E are obtained, broadening thus naturally out an earlier framework considered by this author, the relevant results being namely obtained hitherto only for bQ locally m-convex 1-algebras. 相似文献