首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
Reflexive algebras play a central role in the study of general operator algebras. For a reflexive algebra the associated invariant subspace lattice has structural importance analogous to that of the algebraic commutant in the study of 1-algebras. Tomita's tensor product commutation theorem can be restated in the form Alg(L1 ? L2) = Alg L1 ? Alg L2, where each Li is a reflexive ortho-lattice. This same formula is proved (for n-fold tensor products) in the setting when each Li is a nest. Thus, in particular, a tensor product of nest algebras is again a reflexive algebra. Lance has shown that the Hochschild cohomology of nest algebras vanishes; modifications of his arguments show that cohomology vanishes for arbitrary CSL algebras whose lattices are generated by finitely many independent nests. This appears to be the strongest possible result in this direction. The class of irreducible tridiagonal algebras with finite-width commutative lattices is investigated and it is shown that these algebras have nontrivial first cohomology. Finally, it is shown that if L is a finite-width commutative subspace lattice and K is the set of compact operators then the quasitriangular algebra Alg L + K is closed in the norm topology. This extends to arbitrary finite-width CSL algebras a result obtained for nest algebras by Fall, Arveson, and Muhly.  相似文献   

2.
It will be shown that given any element X in a simple Lie algebra Q over C, there exists a YQ such that the Lie algebra generated by X and Y is Q. The result is extended to the real semisimple Lie algebras. In some sense the main theorem of this paper can be regarded as an extension of Morozov-Jacobson theorem concerning three dimensional simple Lie algebras (see the remark at the end of Sec. 4). A new property of a special class of regular elements, known as the cyclic elements, is given.  相似文献   

3.
We show that for A ranging over n×n circulants with three ones in each row, where n is prime, lim inf|detA|1n>1. For a subfamily containing almost all A's this lim inf is in fact 1.38…. We also compute the permanents of a certain family of matrices.  相似文献   

4.
A uniform algebra A on a compact space X is tight if for each g?C(X), the Hankel-type operator fgf + A from A toCA is weakly compact. Two families of uniform algebras are shown to be tight: the algebras such as R(K) that arise in the theory of rational approximation on compact subsets of the complex plane, and algebras of analytic functions on domains in Cn for which a certain ?-problem is solvable. A couple of characterizations of tight algebras are given, and one of these is used to show that the property of being tight places severe restrictions on the Gleason parts of A and the measures in A.  相似文献   

5.
Conditions are given for Banach algebras U and commutative Banach algebras B which insure that every homomorphism v from U into B is continuous. Similar results are obtained for derivations which either map the algebra U into itself or map the algebra into a suitable U-module.  相似文献   

6.
Considering complete Boolean algebras G as sets of truth values a new concept of compactness—so-called probabilistic compactness — is introduced to G-fuzzy topological spaces. The aim of this paper is to show that the most important theorems of the theory of ordinary compact spaces remain true; e.g. probabilistic compactness is preserved under projective limits, every probabilistic compact space has an unique G-fuzzy uniformity being compatible with the underlying G-fuzzy topology, etc. Finally using the selection theorem due to Kuratowski and Ryll-Nardzewski a non-trivial example of a probabilistic compact space is given.  相似文献   

7.
Given two von Neumann algebras A ?B we study the relation between the existence of an interpolating type I factor F, namely A ?F ?B, the implementability of the flip automorphism of A ? A by a unitary in B ? B, and the statistical independence of A and B′ (A and B′ generate a W1-tensor product). As an application in Q.F.T. we derive in a natural way a structure theorem of Buchholz for the von Neumann algebras of local observables associated to free fields.  相似文献   

8.
We find the automorphisms and the spectra of several different topological convolution algebras of C-functions on the real line. Starting with the convolution algebra of compactly supported C-functions, equipped with the usual LF-topology, we define a corresponding convolution algebra of C-functions of arbitrarily fast exponential decay at ∞; and convolution algebras of a given finite degree r of exponential decay at ∞. These algebras may be described topologically as “hyper Schwartz spaces.” With a natural Frechet topology, which we define, they get a structure as locally m-convex algebras. The continuous automorphisms and spectra of these algebras are described completely. We show that the algebra of C-functions of infinitly fast exponential decay at ∞, H J, on the one hand, and the algebra of C-functions of only a finite degree e?r¦x¦ decay at ∞, Jr0, on the other hand, have quite different automorphisms, although H J = ∩rJr0. As an application, we show that the conformal group is canonically represented as the full group of automorphisms of Jr0, and that this representation does not extend to a representation on the Banach algebra L1(R).  相似文献   

9.
Under what conditions does the spectrum of a topological C-algebra exhibit C-analytic structure? Some sufficient conditions are known for uniform Banach algebras. In this paper, we treat the case of uniform Fréchet-nuclear algebras (=(FN)-algebras). Assume that the spectrum σA of a (FN)-algebra A is locally compact (under the usual Gelfand topology). Then σA carries, in a natural way, the structure of a (DFN)-analytic space (DFN = strong dual of a (FN)-space); we denote it by (σA, A) where A is the sheaf of germs of (DFN)-analytic functions. The notion of (DFN)-analytic spaces is defined in analogy to the one of Douady's Banach-analytic spaces. A ringed space (X, A) ist called uniform if the section algebras A(U) are complete under the topology of compact convergence on U, for all open U ?X.  相似文献   

10.
Let K be a class of finite algebras closed under subalgebras, homomorphic images and finite direct products. It is shown that K is isomorphic to the class of bounded distributive lattices if and only if K is generated by a lattice-primal algebra.  相似文献   

11.
In this paper some new results on analytic domination of operators and on integrability of Lie algebras of operators are proved and then our methods are applied to the study of Lie algebras of unbounded derivations in C1 algebras.  相似文献   

12.
13.
If A is a finite-dimensional associative k-algebra with unit, then its rank R(A), i.e. its bilinear complexity, is never less than 2dimA?#M(A). A is said to be of minimal rank if R(A)=2dimA?#M(A). In this paper we determine for infinite perfect fields k all commutative k-algebras of minimal rank. Roughly speaking, these algebras are built up from simply generated structures which annihilate each other. Furthermore, we indicate how this result can be used to obtain new lower bounds for the rank of specific commutative algebras.  相似文献   

14.
15.
16.
The purpose of this paper is to generalize the following situation: from the concrete structure B, we define the notion of Boolean algebras; the Stone representation theorem allows us to replace the algebraic study of Boolean algebras by a topological one. Let E be a non-empty set, and J a non-empty ordered set. Note B the set of all fuzzy subsets of (E,J). We shall introduce the concept of fuzzy Boolean algebra and find a representation theorem. But it will be difficult to speak of the dual fuzzy topological space of a fuzzy Boolean algebra as we shall see further, except in certain particular cases.  相似文献   

17.
We prove that the pure global dimension of a polynomial ring over an integral domain k in a finite or countable number n?2 of commuting (non-commuting, resp.) variables is t + 1, provided |k| = ?t. As an application, we determine the pure global dimension of wild algebras of quiver type, also (in case k is an algebraically closed field) of the wild local and wild commutative algebras of finite k-dimension.  相似文献   

18.
We show that a derivation of a C1-algebra A is automatically relative bounded with respect to any closed 1derivation of A with smaller domain. We give also some related results on the automatic continuity of derivations in certain Banach algebras.  相似文献   

19.
Let A be a finite-dimensional basic connected associative algebra over an algebraically closed field, and T(A)=A ? DA its trivial extension by its minimal injective cogenerator. We prove that T(A) is representation-finite of Cartan class Δ if and only if A is an iterated tilted algebra of Dynkin class Δ. The proof also yields a construction procedure for iterated tilted algebras of Dynkin type.  相似文献   

20.
We are interested here in the Hochschild cohomology of tensor triangular algebras T. We describe in particular a spectral sequence, whose terms are parametrized by the lengths of the trajectories of the quiver associated with T, and which converges to HH1(T), the Hochschild cohomology of T. Differentials at the first level are sums of cup products. To cite this article: S. Dourlens, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 527–532.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号