共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
David Gurarie 《Journal of Mathematical Analysis and Applications》1985,108(1):223-229
For elliptic operators on Rn and certain of their singular perturbations relative compactness of B with respect to A is established. This result applies to the study of Lp-spectra of elliptic operators for different p. 相似文献
3.
Peter B. Wilson 《Linear algebra and its applications》1975,10(1):7-18
Given a normal matrix A, asymptotic bounds are obtained for in terms of the spectral radius of A, the number of eigenvalues of A with modulus equal to the spectral radius of A, and the order of A. These results are extended to provide bounds for for all m ? 1. 相似文献
4.
Let A be an n×n complex matrix. For a suitable subspace of Cn the Schur compression A and the (generalized) Schur complement A/ are defined. If A is written in the form according to the decomposition and if B is invertible, then and The commutativity rule for Schur complements is proved: This unifies Crabtree and Haynsworth's quotient formula for (classical) Schur complements and Anderson's commutativity rule for shorted operators. Further, the absorption rule for Schur compressions is proved: . 相似文献
5.
C.J.K Batty 《Journal of Functional Analysis》1984,57(3):233-243
Let (A, G, α) be a C1-dynamical system, where G is abelian, and let φ be an invariant state. Suppose that there is a neighbourhood Ω of the identity in and a finite constant κ such that whenever xi lies in a spectral subspace , where . This condition of complete spectral passivity, together with self-adjointness of the left kernel of φ, ensures that φ satisfies the KMS condition for some one-parameter subgroup of G. 相似文献
6.
For 1 ? p ? ∞, let , be the lp norm of an m × n complex A = (αij) ?Cm × n. The main purpose of this paper is to find, for any p, q ? 1, the best (smallest) possible constants τ(m, k, n, p, q) and σ(m, k, n, p, q) for which inequalities of the form hold for all A?Cm × k, B?Ck × n. This leads to upper bounds for inner products on Ck and for ordinary lp operator norms on Cm × n. 相似文献
7.
Raul Cordovil 《Journal of Combinatorial Theory, Series B》1983,34(2):209-223
A natural sufficient condition for a finite family of single element extensions of a matroid to be compatible is given. Characterizations of all the finite extensions N of a matroid M(E) are given for which the rank function satisfies or equivalently the closure operator satisfies . The single element extensions and the principal extensions are examples of such matroids. The notion of a sheaf of flats of M. Las Vergnas is used in the proof of a new necessary and sufficient condition for two single element extensions of a matroid to be compatible. An initial announcement of part of these results appeared in R. Cordovil (C. R. Acad. Sci. Paris. A284 (1977), 1249–1252). 相似文献
8.
Anne Marie Torpe 《Journal of Functional Analysis》1985,61(1):15-71
The K-theory of the C1-algebra associated to C∞-foliations (V, F) of a manifold V in the simplest non-trivial case, i.e., dim V = 2, is studied. Since the case of the Kronecker foliation was settled by Pimsner and Voiculescu (J. Operator Theory4 (1980), 93–118), the remaining problem deals with foliations by Reeb components. The K-theory of for the Reeb foliation of S3 is also computed. In these cases the C1-algebra is obtained from simpler C1-algebras by means of pullback diagrams and short exact sequences. The K-groups are computed using the associated Mayer-Vietoris and six-term exact sequences. The results characterize the C1-algebra of the Reeb foliation of 2 uniquely as an extension of C(S1) by C(S1). For the foliations of 2 it is found that the K-groups count the number of Reeb components separated by stable compact leaves. A C∞-foliation of 2 such that K1(C1(2, F)) has infinite rank is also constructed. Finally it is proved, by explicit calculation using (M. Penington, “K-Theory and C1-Algebras of Lie Groups and Foliations,” D. Phil. thesis, Oxford, 1983), that the natural map is an isomorphism for foliations by Reeb components of 2 and S3. In particular this proves the Baum-Connes conjecture (P. Baum and A. Connes, Geometric K-theory for Lie groups, preprint, 1982; A. Connes, Proc. Symp. Pure Math.38 (1982), 521–628) when V = 2. 相似文献
9.
Let Ω = {1, 0} and for each integer n ≥ 1 let (n-tuple) and for all k = 0,1,…,n. Let {Ym}m≥1 be a sequence of i.i.d. random variables such that . For each A in , let TA be the first occurrence time of A with respect to the stochastic process {Ym}m≥1. R. Chen and A.Zame (1979, J. Multivariate Anal. 9, 150–157) prove that if n ≥ 3, then for each element A in , there is an element B in such that the probability that TB is less than TA is greater than . This result is sharpened as follows: (I) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A in , there is an element B also in such that the probability that TB is less than TA is greater than ; (II) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A = (a1, a2,…,an) in , there is an element C also in such that the probability that TA is less than TC is greater than if n ≠ 2m or n = 2m but ai = ai + 1 for some 1 ≤ i ≤ n?1. These new results provide us with a better and deeper understanding of the fair coin tossing process. 相似文献
10.
Let A be an arbitrary n×n matrix, partitioned so that if A=[Aij], then all submatrices Aii are square. If x is a positive vector, it is well-known that , where , contains all the eigenvalues of A. The purpose of this paper is to give a new definition of the concept of an isolated subregion of G(x). An algorithm is given for obtaining the best such isolated subregion in a certain sense, and examples are given to show that tighter bounds for some eigenvalues of A may be obtained than with previous algorithms. For ease of computation, each subregion Gi(x) is replaced by the union of circular disks centered at the eigenvalues of Aii. 相似文献
11.
A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces
P.D Smith 《Journal of Differential Equations》1984,53(2):125-138
The compactness method to weighted spaces is extended to prove the following theorem:Let H2,s1(B1) be the weighted Sobolev space on the unit ball in Rn with norm Let n ? 2 ? s < n. Let u? [H2,s1(B1) ∩ L∞(B1)]N be a solution of the nonlinear elliptic system , are uniformly continuous functions of their arguments and satisfy: . Then there exists an R1, 0 < R1 < 1, and an α, 0 < α < 1, along with a set such that (1) , (2) Ω does not contain the origin; Ω does not contain BR1, (3) is open, (4) u is ; u is LipαBR1. 相似文献
12.
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
13.
14.
Necessary and sufficient conditions for a solution {zk} of the difference equation , with singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, , are given first. In particular, the case when and is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed. 相似文献
15.
16.
Let the n × n complex matrix A have complex eigenvalues λ1,λ2,…λn. Upper and lower bounds for Σ(Reλi)2 are obtained, extending similar bounds for Σ|λi|2 obtained by Eberlein (1965), Henrici (1962), and Kress, de Vries, and Wegmann (1974). These bounds involve the traces of A1A, B2, C2, and D2, where , , and , and strengthen some of the results in our earlier paper “Bounds for eigenvalues using traces” in Linear Algebra and Appl. [12]. 相似文献
17.
Alladi Sitaram 《Journal of Functional Analysis》1978,27(2):179-184
Let G be a semisimple noncompact Lie group with finite center and let K be a maximal compact subgroup. Then W. H. Barker has shown that if T is a positive definite distribution on G, then T extends to Harish-Chandra's Schwartz space 1(G). We show that the corresponding property is no longer true for the space of double cosets . If G is of real-rank 1, we construct liner functionals for each p, 0 < p ? 2, such that but Tp does not extend to a continuous functional on . In particular, if p ? 1, Tv does not extend to a continuous functional on . We use this to answer a question (in the negative) raised by Barker whether for a K-bi-invariant distribution T on G to be positive definite it is enough to verify that . The main tool used is a theorem of Trombi-Varadarajan. 相似文献
18.
Let and be polynomials with real zeros satisfying An?1 = Bn?1 = 0, and let Using the recently proved validity of the van der Waerden conjecture on permanents, some results on the real zeros of H(x) are obtained. These results are related to classical results on composite polynomials. 相似文献
19.
Gideon Nettler 《Journal of Number Theory》1981,13(4):456-462
In a previous paper it was proven that given the continued fractions where the a's and b's are positive integers, then A, B, A ± B, and AB are irrational numbers if for all n sufficiently large, and transcendental numbers if for all n sufficiently large. Using a more direct approach it is proven in this paper that A, B, A ± B, and AB are transcendental numbers if an > bn > an?1(n?1)2 for all n sufficiently large. 相似文献
20.
Christopher Lance 《Journal of Functional Analysis》1973,12(2):157-176
A C1-algebra is called nuclear if there is a unique way of forming its tensor product with any other C1-algebra. Takesaki [17] showed that all C1-algebras of type I and all inductive limits of such algebras are nuclear, but that the C1-algebra generated by the left regular representation of G on l2(G) is nonnuclear, where G is the free group on two generators. In this paper an extension property for tensor products of C1-algebras is introduced, and is characterized in terms of the existence of a certain family of weak expectations on the algebra. Nuclearity implies the extension property, and this is used to show that for a discrete group is nuclear if and only if G is amenable.An approximation property in the dual of a C1-algebra is introduced, and shown to imply nuclearity. It is not clear whether the converse implication holds, but it is proved that the known nuclear C1-algebras satisfy the approximation property. 相似文献