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1.
Steen Pedersen 《Proceedings of the American Mathematical Society》2004,132(7):2095-2101
Suppose that where are real numbers such that and The union is not assumed to be disjoint. It is shown that the translates , , tile the real line for some bounded measurable set if and only if the exponentials , , form an orthogonal basis for some bounded measurable set
2.
We study the linear functional on the Cuntz algebra associated to a sequence of unit vectors in that is a generalization of the Cuntz state. We prove that is positive if and only if is a constant sequence.
3.
Let be a nontrivial dilation. We show that every complete norm on that makes from into itself continuous is equivalent to . also determines the norm of both and with in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on .
4.
Colin C. Graham 《Proceedings of the American Mathematical Society》2004,132(7):1963-1971
Theorem. If are perfect compact subsets of the locally compact metrizable abelian group, then there are pairwise disjoint perfect subsets such that (i) is either a Kronecker set or (ii) for some , is a translate of a -set all of whose elements have order , and (iii) is isomorphic to the projective tensor product .
This extends what was previously known for groups such as or for the case to the general locally compact abelian group. Old results concerning the local existence of Kronecker and -sets are improved.
5.
Dejan Kolaric 《Proceedings of the American Mathematical Society》2008,136(4):1273-1284
Let be a closed polydisc or ball in , and let be a quasi-projective algebraic manifold which is Zariski locally equivalent to , or a complement of an algebraic subvariety of codimension in such a manifold. If is an integer satisfying , then every holomorphic map from a neighborhood of to with rank at every point of can be approximated uniformly on by entire maps with rank at every point of .
6.
Lourdes Juan 《Proceedings of the American Mathematical Society》2004,132(9):2549-2556
Given a connected linear algebraic group over an algebraically closed field of characteristic 0, we construct a pure Picard-Vessiot extension for , namely, a Picard-Vessiot extension , with differential Galois group , such that and are purely differentially transcendental over . The differential field is the quotient field of a -stable proper differential subring with the property that if is any differential field with field of constants and is a Picard-Vessiot extension with differential Galois group a connected subgroup of , then there is a differential homomorphism such that is generated over as a differential field by .
7.
Huaquan Wei Yanming Wang Yangming Li 《Proceedings of the American Mathematical Society》2004,132(8):2197-2204
This paper proves: Let be a saturated formation containing . Suppose that is a group with a normal subgroup such that .
(1) If all maximal subgroups of any Sylow subgroup of are -supple- mented in , then ;
(2) If all minimal subgroups and all cyclic subgroups with order 4 of are -supplemented in , then .
8.
Scott Armstrong Ken Dykema Ruy Exel Hanfeng Li 《Proceedings of the American Mathematical Society》2004,132(7):2019-2030
We examine the question of when the -homomorphism of full amalgamated free product C-algebras, arising from compatible inclusions of C-algebras , and , is an embedding. Results giving sufficient conditions for to be injective, as well as classes of examples where fails to be injective, are obtained. As an application, we give necessary and sufficient conditions for the full amalgamated free product of finite-dimensional C-algebras to be residually finite dimensional.
9.
Sandy Grabiner 《Proceedings of the American Mathematical Society》2004,132(6):1675-1684
Suppose that is a weighted convolution algebra on with the weight normalized so that the corresponding space of measures is the dual space of the space of continuous functions. Suppose that is a continuous nonzero homomorphism, where is also a convolution algebra. If is norm dense in , we show that is (relatively) weak dense in , and we identify the norm closure of with the convergence set for a particular semigroup. When is weak continuous it is enough for to be weak dense in . We also give sufficient conditions and characterizations of weak continuity of . In addition, we show that, for all nonzero in , the sequence converges weak to 0. When is regulated, converges to 0 in norm.
10.
Qian Guohua 《Proceedings of the American Mathematical Society》2004,132(7):1899-1903
Let be a finite group and the largest irreducible character degree of . In this note, we show the following results: if , then ; if and, in addition, is -solvable with abelian Sylow -subgroup, then .
11.
William D. Banks Asma Harcharras 《Proceedings of the American Mathematical Society》2004,132(7):2121-2125
We show that if the norm of an idempotent Schur multiplier on the Schatten class lies sufficiently close to , then it is necessarily equal to . We also give a simple characterization of those idempotent Schur multipliers on whose norm is .
12.
Mamoru Furuya Hiroshi Niitsuma 《Proceedings of the American Mathematical Society》2004,132(11):3189-3193
We introduce the concept of -adic -basis as an extension of the concept of -basis. Let be a regular local ring of prime characteristic and a ring such that . Then we prove that is a regular local ring if and only if there exists an -adic -basis of and is Noetherian.
13.
Let , , be a bounded smooth connected open set and be a map satisfying the hypotheses (H1)-(H4) below. Let with , in and with be two weak solutions of
Suppose that in . Then we show that u_1$"> in under the following assumptions: either u_1$"> on , or on and in . We also show a measure-theoretic version of the Strong Comparison Principle.
Suppose that in . Then we show that u_1$"> in under the following assumptions: either u_1$"> on , or on and in . We also show a measure-theoretic version of the Strong Comparison Principle.
14.
Hal Schenck 《Proceedings of the American Mathematical Society》2004,132(12):3509-3512
Associated to an -dimensional integral convex polytope is a toric variety and divisor , such that the integral points of represent . We study the free resolution of the homogeneous coordinate ring as a module over . It turns out that a simple application of Green's theorem yields good bounds for the linear syzygies of a projective toric surface. In particular, for a planar polytope , satisfies Green's condition if contains at least lattice points.
15.
Let be a commutative noetherian local ring of prime characteristic. Denote by the ring regarded as an -algebra through -times composition of the Frobenius map. Suppose that is F-finite, i.e., is a finitely generated -module. We prove that is Cohen-Macaulay if and only if the -modules have finite Cohen-Macaulay dimensions for infinitely many integers .
16.
Sebastian J. Schreiber 《Proceedings of the American Mathematical Society》2004,132(10):3047-3053
Maps of the nonnegative cone of into itself are considered where are nonnegative, primitive matrices with nondecreasing entries and at least one increasing entry. Let denote the dominant eigenvalue of and . These maps are shown to exhibit a dynamical trichotomy. First, if , then for all nonzero . Second, if , then for all . Finally, if and 1$">, then there exists a compact invariant hypersurface separating . For below , , while for above, . An application to nonlinear Leslie matrices is given.
17.
Edoardo Ballico Changho Keem Seungsuk Park 《Proceedings of the American Mathematical Society》2004,132(11):3153-3158
Let be a smooth projective algebraic curve of genus and an integer with . For all integers we prove the existence of a double covering with a smooth curve of genus and the existence of a degree morphism that does not factor through . By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound ).
18.
Reza Sazeedeh 《Proceedings of the American Mathematical Society》2004,132(10):2885-2891
In this paper we assume that is a Gorenstein Noetherian ring. We show that if is also a local ring with Krull dimension that is less than or equal to 2, then for any nonzero ideal of , is Gorenstein injective. We establish a relation between Gorenstein injective modules and local cohomology. In fact, we will show that if is a Gorenstein ring, then for any -module its local cohomology modules can be calculated by means of a resolution of by Gorenstein injective modules. Also we prove that if is -Gorenstein, is a Gorenstein injective and is a nonzero ideal of , then is Gorenstein injective.
19.
Vassilis Kanellopoulos 《Proceedings of the American Mathematical Society》2004,132(11):3231-3242
W. T. Gowers' theorem asserts that for every Lipschitz function and 0$">, there exists an infinite-dimensional subspace of such that the oscillation of on is at most . The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.
20.
Jingbo Xia 《Proceedings of the American Mathematical Society》2008,136(4):1375-1384
Consider Hankel operators and on the unit sphere in . If , then a necessary condition for to be compact is . We show that when , this condition is no longer necessary for to be compact.