共查询到20条相似文献,搜索用时 353 毫秒
1.
Piotr Grzeszczuk Malgorzata Hryniewicka 《Proceedings of the American Mathematical Society》2007,135(8):2381-2389
Let be an -module algebra, where is a pointed Hopf algebra acting on finitely of dimension . Suppose that for every nonzero -stable left ideal of . It is proved that if satisfies a polynomial identity of degree , then satisfies a polynomial identity of degree provided at least one of the following additional conditions is fulfilled:
- is semiprime and is almost central in ,
- is reduced.
2.
We investigate the problem of the uniqueness of the extension of -homogeneous polynomials in Banach spaces. We show in particular that in a nonreflexive Banach space that admits contractive projection of finite rank of at least dimension 2, for every there exists an -homogeneous polynomial on that has infinitely many extensions to . We also prove that under some geometric conditions imposed on the norm of a complex Banach lattice , for instance when satisfies an upper -estimate with constant one for some , any -homogeneous polynomial on attaining its norm at with a finite rank band projection , has a unique extension to its bidual . We apply these results in a class of Orlicz sequence spaces.
3.
Pietro Aiena Jesú s R. Guillen 《Proceedings of the American Mathematical Society》2007,135(8):2443-2451
A bounded linear operator on a Banach space is said to satisfy ``Weyl's theorem' if the complement in the spectrum of the Weyl spectrum is the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this paper we show that if is a paranormal operator on a Hilbert space, then satisfies Weyl's theorem for every algebraic operator which commutes with .
4.
I. M. Isaacs 《Proceedings of the American Mathematical Society》2008,136(7):2299-2301
Let be the subgroup of generated by all elements that lie in conjugacy classes of the two smallest sizes. Avinoam Mann showed that if is nilpotent, then has nilpotence class at most . Using a slight variation on Mann's methods, we obtain results that do not require us to assume that is nilpotent. We show that if is supersolvable, then is nilpotent with class at most , and in general, the Fitting subgroup of has class at most .
5.
Javier Duoandikoetxea Luis Vega 《Proceedings of the American Mathematical Society》2007,135(9):2795-2802
We obtain conditions on the measure so that the -norm of a function is controlled by the -norms of the function and its gradient. Applications to eigenvalues of the Schrödinger operator and to other inequalites are also given.
6.
Anders J. Frankild Sean Sather-Wagstaff 《Proceedings of the American Mathematical Society》2008,136(7):2303-2312
Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the following result. Let be a commutative noetherian ring and an ideal in the Jacobson radical of . Let be the -adic completion of . If is a finitely generated -module such that for all , then is -adically complete.
7.
It is an observation due to J. J. Kohn that for a smooth bounded pseudoconvex domain in there exists such that the -Neumann operator on maps (the space of -forms with coefficient functions in -Sobolev space of order ) into itself continuously. We show that this conclusion does not hold without the smoothness assumption by constructing a bounded pseudoconvex domain in , smooth except at one point, whose -Neumann operator is not bounded on for any .
8.
This paper presents a property of geometric and topological nature of Gateaux differentiability points and Fréchet differentiability points of almost CL-spaces. More precisely, if we denote by a maximal convex set of the unit sphere of a CL-space , and by the cone generated by , then all Gateaux differentiability points of are just n-s, and all Fréchet differentiability points of are (where n-s denotes the non-support points set of ).
9.
Kathleen L. Petersen 《Proceedings of the American Mathematical Society》2008,136(7):2387-2393
Let be a number field with real places and complex places, and let be the ring of integers of . The quotient has cusps, where is the class number of . We show that under the assumption of the generalized Riemann hypothesis that if is not or an imaginary quadratic field and if , then has infinitely many maximal subgroups with cusps. A key element in the proof is a connection to Artin's Primitive Root Conjecture.
10.
Gregory Lupton Samuel Bruce Smith 《Proceedings of the American Mathematical Society》2007,135(8):2649-2659
We compute the rank of the fundamental group of any connected component of the space for and connected, nilpotent CW complexes of finite type with finite. For the component corresponding to a general homotopy class , we give a formula directly computable from the Sullivan model for . For the component of the constant map, our formula retrieves a known expression for the rank in terms of classical invariants of and . When both and are rationally elliptic spaces with positive Euler characteristic, we use our formula to determine the rank of the fundamental group of any component of explicitly in terms of the homomorphism induced by on rational cohomology.
11.
M. Hellus 《Proceedings of the American Mathematical Society》2008,136(7):2313-2321
For a Noetherian ring we call an -module cofinite if there exists an ideal of such that is -cofinite; we show that every cofinite module satisfies . As an application we study the question which local cohomology modules satisfy . There are two situations where the answer is positive. On the other hand, we present two counterexamples, the failure in these two examples coming from different reasons.
12.
We consider an invertible operator on a Banach space whose spectrum is an interpolating set for Hölder classes. We show that if , , with and , then for all , assuming that satisfies suitable regularity conditions. When is a Hilbert space and (i.e. is a contraction), we show that under the same assumptions, is unitary and this is sharp.
13.
Paola Bonacini 《Proceedings of the American Mathematical Society》2008,136(7):2289-2297
If is an integral curve and an algebraically closed field of characteristic 0, it is known that the points of the general plane section of are in uniform position. From this it follows easily that the general minimal curve containing is irreducible. If char, the points of may not be in uniform position. However, we prove that the general minimal curve containing is still irreducible.
14.
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.
15.
Daria Michalik 《Proceedings of the American Mathematical Society》2007,135(8):2661-2664
We give a short proof of the following fact: the set of embeddings of any -dimensional separable metric space into a certain -dimensional subset of the -product of Sierpinski curves is residual in .
16.
Dusan Repovs Boaz Tsaban Lyubomyr Zdomskyy 《Proceedings of the American Mathematical Society》2008,136(7):2515-2520
We show that even for subsets of the real line that do not contain perfect sets, the Hurewicz property does not imply the property , asserting that for each countable family of open -covers of , there is a choice function whose image is a -cover of . This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the second author, and implies that for , the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskiı's property .
17.
Let be a local complete ring. For an -module the canonical ring map is in general neither injective nor surjective; we show that it is bijective for every local cohomology module if for every ( an ideal of ); furthermore the same holds for the Matlis dual of such a module. As an application we prove new criteria for an ideal to be a set-theoretic complete intersection.
18.
Francisco-Javier Turiel 《Proceedings of the American Mathematical Society》2007,135(8):2665-2667
We construct, for every even dimensional sphere , , and every odd integer , a homogeneous polynomial map of Brouwer degree and algebraic degree .
19.
S. V. Borodachov D. P. Hardin E. B. Saff 《Proceedings of the American Mathematical Society》2007,135(8):2369-2380
We investigate the asymptotic behavior, as grows, of the largest minimal pairwise distance of points restricted to an arbitrary compact rectifiable set embedded in Euclidean space, and we find the limit distribution of such optimal configurations. For this purpose, we compare best-packing configurations with minimal Riesz -energy configurations and determine the -th root asymptotic behavior (as of the minimal energy constants.
We show that the upper and the lower dimension of a set defined through the Riesz energy or best-packing coincides with the upper and lower Minkowski dimension, respectively.
For certain sets in of integer Hausdorff dimension, we show that the limiting behavior of the best-packing distance as well as the minimal -energy for large is different for different subsequences of the cardinalities of the configurations.
20.
Darryl McCullough 《Proceedings of the American Mathematical Society》2003,131(7):2247-2253
Fix a free, orientation-preserving action of a finite group on a -dimensional handlebody . Whenever acts freely preserving orientation on a connected -manifold , there is a -equivariant imbedding of into . There are choices of closed and Seifert-fibered for which the image of is a handlebody of a Heegaard splitting of . Provided that the genus of is at least , there are similar choices with closed and hyperbolic.