共查询到10条相似文献,搜索用时 93 毫秒
1.
Manuel Gonzá lez Mostafa Mbekhta Mourad Oudghiri 《Proceedings of the American Mathematical Society》2008,136(10):3521-3528
For a bounded operator acting on a complex Banach space, we show that if is not surjective, then is an isolated point of the surjective spectrum of if and only if , where is the quasinilpotent part of and is the analytic core for . Moreover, we study the operators for which . We show that for each of these operators , there exists a finite set consisting of Riesz points for such that and is connected, and derive some consequences.
2.
Martin Hertweck 《Proceedings of the American Mathematical Society》2008,136(5):1539-1547
For finite nilpotent groups and , and a -adapted ring (the rational integers, for example), it is shown that any isomorphism between the centers of the group rings and is monomial, i.e., maps class sums in to class sums in up to multiplication with roots of unity. As a consequence, and have identical character tables if and only if the centers of their integral group rings and are isomorphic. In the course of the proof, a new proof of the class sum correspondence is given.
3.
Natasha Dobrinen 《Proceedings of the American Mathematical Society》2008,136(5):1815-1821
Suppose are models of ZFC with the same ordinals, and that for all regular cardinals in , satisfies . If contains a sequence for some ordinal , then for all cardinals in with regular in and , is stationary in . That is, a new -sequence achieves global co-stationarity of the ground model.
4.
Wendy Lowen 《Proceedings of the American Mathematical Society》2008,136(9):3045-3050
For a scheme , we construct a sheaf of complexes on such that for every quasi-compact open , is quasi-isomorphic to the Hochschild complex of (Lowen and Van den Bergh, 2005). Since is moreover acyclic for taking sections on quasi-compact opens, we obtain a local to global spectral sequence for Hochschild cohomology if is quasi-compact.
5.
Jin Xi Chen Zi Li Chen Ngai-Ching Wong 《Proceedings of the American Mathematical Society》2008,136(11):3869-3874
Let and be compact Hausdorff spaces, and , be Banach lattices. Let denote the Banach lattice of all continuous -valued functions on equipped with the pointwise ordering and the sup norm. We prove that if there exists a Riesz isomorphism such that is non-vanishing on if and only if is non-vanishing on , then is homeomorphic to , and is Riesz isomorphic to . In this case, can be written as a weighted composition operator: , where is a homeomorphism from onto , and is a Riesz isomorphism from onto for every in . This generalizes some known results obtained recently.
6.
Phil Hanlon 《Proceedings of the American Mathematical Society》2008,136(11):3741-3749
Let be a simple graph with nodes. The coloring complex of , as defined by Steingrimsson, has -faces consisting of all ordered set partitions, in which at least one contains an edge of . Jonsson proved that the homology of the coloring complex is concentrated in the top degree. In addition, Jonsson showed that the dimension of the top homology is one less than the number of acyclic orientations of .
In this paper, we show that the Eulerian idempotents give a decomposition of the top homology of into components . We go on to prove that the dimensions of the Hodge pieces of the homology are equal to the absolute values of the coefficients of the chromatic polynomial of . Specifically, if we write , then .
7.
Yan-Ni Chen Hong-Ke Du Hai-Yan Zhang 《Proceedings of the American Mathematical Society》2008,136(10):3483-3492
Let and be two idempotents on a Hilbert space. In 2005, J. Giol in [Segments of bounded linear idempotents on a Hilbert space, J. Funct. Anal. 229(2005) 405-423] had established that, if is invertible, then and are homotopic with In this paper, we have given a necessary and sufficient condition that where denotes the minimal number of segments required to connect not only from to , but also from to in the set of idempotents.
8.
Dimas José Gonç alves Plamen Koshlukov 《Proceedings of the American Mathematical Society》2008,136(8):2711-2717
Let be an algebraically closed field of characteristic 0, and let be the infinite dimensional Grassmann (or exterior) algebra over . Denote by the vector space of the multilinear polynomials of degree in , ..., in the free associative algebra . The symmetric group acts on the left-hand side on , thus turning it into an -module. This fact, although simple, plays an important role in the theory of PI algebras since one may study the identities satisfied by a given algebra by applying methods from the representation theory of the symmetric group. The -modules and are canonically isomorphic. Letting be the alternating group in , one may study and its isomorphic copy in with the corresponding action of . Henke and Regev described the -codimensions of the Grassmann algebra , and conjectured a finite generating set of the -identities for . Here we answer their conjecture in the affirmative.
9.
Lou van den Dries 《Proceedings of the American Mathematical Society》2008,136(10):3435-3448
About a year ago Angus Macintyre raised the following question. Let and be complete local noetherian rings with maximal ideals and such that is isomorphic to for every . Does it follow that and are isomorphic? We show that the answer is yes if the residue field is algebraic over its prime field. The proof uses a strong approximation theorem of Pfister and Popescu, or rather a variant of it, which we obtain by a method due to Denef and Lipshitz. Examples by Gabber show that the answer is no in general.
10.
Istvá n Juhá sz Zoltá n Szentmikló ssy 《Proceedings of the American Mathematical Society》2008,136(8):2979-2984
All spaces below are Tychonov. We define the projective - character of a space as the supremum of the values where ranges over all (Tychonov) continuous images of . Our main result says that every space has a -base whose order is ; that is, every point in is contained in at most -many members of the -base. Since for compact , this is a significant generalization of a celebrated result of Shapirovskii.