共查询到20条相似文献,搜索用时 31 毫秒
1.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Proceedings of the American Mathematical Society》2006,134(11):3319-3327
Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.
2.
Ping Wong Ng 《Proceedings of the American Mathematical Society》2006,134(8):2223-2228
Let be a unital, simple, separable -algebra with real rank zero, stable rank one, and weakly unperforated ordered group. Suppose, also, that can be locally approximated by type I algebras with Hausdorff spectrum and bounded irreducible representations (the bound being dependent on the local approximating algebra). Then is tracially approximately finite dimensional (i.e., has tracial rank zero).
Hence, is an -algebra with bounded dimension growth and is determined by -theoretic invariants.
The above result also gives the first proof for the locally case.
3.
Francesca Astengo Bianca Di Blasio 《Proceedings of the American Mathematical Society》2006,134(5):1319-1329
The generalised Cayley transform from an Iwasawa -group into the corresponding real unit sphere induces isomorphisms between suitable Sobolev spaces and . We study the differential of , and we obtain a criterion for a function to be in .
4.
Janko Marovt 《Proceedings of the American Mathematical Society》2006,134(4):1065-1075
Let be a compact Hausdorff space which satisfies the first axiom of countability, let and let , be the set of all continuous functions from to If , ,is a bijective multiplicative map, then there exist a homeomorphism and a continuous map such that for all and for all
5.
Gustavo Corach Alejandra Maestripieri Demetrio Stojanoff 《Proceedings of the American Mathematical Society》2006,134(3):765-778
If is a Hilbert space, is a positive bounded linear operator on and is a closed subspace of , the relative position between and establishes a notion of compatibility. We show that the compatibility of is equivalent to the existence of a convenient orthogonal projection in the operator range with its canonical Hilbertian structure.
6.
We show that the -algebra associated to the tail-equivalence relation on a Bratteli diagram, according to a procedure recently introduced by the first-named author and A. Lopes, is isomorphic to the -algebra of the diagram. More generally we consider an approximately proper equivalence relation on a compact space for which the quotient maps are local homeomorphisms. We show that the algebra associated to under the above-mentioned procedure is isomorphic to the groupoid -algebra .
7.
Dimitri Leemans 《Proceedings of the American Mathematical Society》2006,134(12):3649-3651
Let , with an odd power of two. For each almost simple group such that , we prove that is not a C-group and therefore is not the automorphism group of an abstract regular polytope. For , we show that there is always at least one abstract regular polytope such that . Moreover, if is an abstract regular polytope such that , then is a polyhedron.
8.
Isabelle Chalendar Jonathan R. Partington 《Proceedings of the American Mathematical Society》2006,134(5):1391-1396
Let be a separable Banach space and a sequence of closed subspaces of satisfying for all . We first prove the existence of a dense-range and injective compact operator such that each is a dense subset of , solving a problem of Yahaghi (2004). Our second main result concerns isomorphic and dense-range injective compact mappings between dense sets of linearly independent vectors, extending a result of Grivaux (2003).
9.
Vigleik Angeltveit 《Proceedings of the American Mathematical Society》2008,136(7):2323-2332
We define the notion of an enriched Reedy category and show that if is a -Reedy category for some symmetric monoidal model category and is a -model category, the category of -functors and -natural transformations from to is again a model category.
10.
E. Serrano C. Piñ eiro J. M. Delgado 《Proceedings of the American Mathematical Society》2006,134(3):689-695
Let and be Banach spaces. We say that a set denotes the space of all compact operators from into ) is equicompact if there exists a null sequence in such that for all and all . It is easy to show that collectively compactness and equicompactness are dual concepts in the following sense: is equicompact iff is collectively compact. We study some properties of equicompact sets and, among other results, we prove: 1) a set is equicompact iff each bounded sequence in has a subsequence such that is a converging sequence uniformly for ; 2) if does not have finite cotype and is a maximal equicompact set, then, given and a finite set in , there is an operator such that for and all .
11.
Eui-Chai Jeong 《Proceedings of the American Mathematical Society》2006,134(1):99-104
For a pure state on , which is an extension of a pure state on with the property that if is a corresponding representation, then , induces a unital shift of of the Powers index . We describe states on by using sequences of unit vectors in . We study the linear functionals on the Cuntz algebra whose restrictions are the product pure state on . We find conditions on the sequence of unit vectors for which the corresponding linear functionals on become states under these conditions.
12.
Yifeng Xue 《Proceedings of the American Mathematical Society》2007,135(3):705-711
A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).
13.
T. Kalmes 《Proceedings of the American Mathematical Society》2006,134(10):2997-3002
A -semigroup on a Banach space is called hypercyclic if there exists an element such that is dense in . is called chaotic if is hypercyclic and the set of its periodic vectors is dense in as well. We show that a spectral condition introduced by Desch, Schappacher and Webb requiring many eigenvectors of the generator which depend analytically on the eigenvalues not only implies the chaoticity of the semigroup but the chaoticity of every . Furthermore, we show that semigroups whose generators have compact resolvent are never chaotic. In a second part we prove the existence of hypercyclic vectors in for a hypercyclic semigroup , where is its generator.
14.
Y. Kinoshita K. Nishida Y. Yamanaka A. Yoneda 《Proceedings of the American Mathematical Society》2006,134(12):3437-3444
Let be a multiplicative filtration of a local ring such that the Rees algebra is Noetherian. We recall Burch's inequality for and give an upper bound of the a-invariant of the associated graded ring using a reduction system of . Applying those results, we study the symbolic Rees algebra of certain ideals of dimension .
15.
Dong Zhe 《Proceedings of the American Mathematical Society》2007,135(1):191-200
In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in the Alg-module is initiated, where is a completely distributive subspace lattice on a Hilbert space . Furthermore, as an application of single elements, we study module isomorphisms between norm closed Alg-modules, where is a nest, and obtain the following result: Suppose that are norm closed Alg-modules and that is a module isomorphism. Then and there exists a non-zero complex number such that .
16.
Nuria Corral Percy Ferná ndez-Sá nchez 《Proceedings of the American Mathematical Society》2006,134(4):1125-1132
We bound the equisingularity type of the set of isolated separatrices of a holomorphic foliation of in terms of the Milnor number of . This result gives a bound for the degree of an algebraic invariant curve of a foliation of in terms of the degree of , provided that all the branches of are isolated separatrices.
17.
Boaz Tsaban 《Proceedings of the American Mathematical Society》2006,134(3):881-891
We construct several topological groups with very strong combinatorial properties. In particular, we give simple examples of subgroups of (thus strictly -bounded) which have the Menger and Hurewicz properties but are not -compact, and show that the product of two -bounded subgroups of may fail to be -bounded, even when they satisfy the stronger property . This solves a problem of Tkacenko and Hernandez, and extends independent solutions of Krawczyk and Michalewski and of Banakh, Nickolas, and Sanchis. We also construct separable metrizable groups of size continuum such that every countable Borel -cover of contains a -cover of .
18.
Phil Hanlon 《Proceedings of the American Mathematical Society》2006,134(7):1857-1867
Let be a poset with unique minimal and maximal elements and . For each , let be the vector space spanned by -chains from to in . We define the notion of a Hodge structure on which consists of a local action of on , for each , such that the boundary map intertwines the actions of and according to a certain condition.
We show that if has a Hodge structure, then the families of Eulerian idempotents intertwine the boundary map, and so we get a splitting of into Hodge pieces.
We consider the case where is , the poset of subsets of with cardinality divisible by is fixed, and is a multiple of . We prove a remarkable formula which relates the characters of acting on the Hodge pieces of the homologies of the to the characters of acting on the homologies of the posets of partitions with every block size divisible by .
19.
Edgar E. Enochs J. R. Garcí a Rozas Luis Oyonarte 《Proceedings of the American Mathematical Society》2000,128(10):2863-2868
We prove that for certain classes of modules such that direct sums of -covers ( -envelopes) are -covers ( -envelopes), -covering ( -enveloping) homomorphisms are always right (left) minimal. As a particular case we see that over noetherian rings, essential monomorphisms are left minimal. The same type of results are given when direct products of -covers are -covers. Finally we prove that over commutative noetherian rings, any direct product of flat covers of modules of finite length is a flat cover. 相似文献
20.
Mohammad B. Asadi A. Khosravi 《Proceedings of the American Mathematical Society》2006,134(11):3255-3256
This study provides an elementary proof of the well-known fact that any isomorphism of standard operator algebras on normed spaces , respectively, is spatial; i.e., there exists a topological isomorphism such that for any . In particular, is continuous.