共查询到20条相似文献,搜索用时 15 毫秒
1.
Moonja Jeong Masahiko Taniguchi 《Proceedings of the American Mathematical Society》2003,131(8):2325-2328
In this paper, we solve a conjecture of S. Bell (1992) affirmatively. Actually, we prove that every non-degenerate -connected planar domain , where 1$">is representable as with a suitable rational function of degree . This result is considered as a natural generalization of the classical Riemann mapping theorem for simply connected planar domains.
2.
Liana M. Sega 《Proceedings of the American Mathematical Society》2003,131(8):2313-2323
We prove that if , are finite modules over a Gorenstein local ring of codimension at most , then the vanishing of for is equivalent to the vanishing of for . Furthermore, if has no embedded deformation, then such vanishing occurs if and only if or has finite projective dimension.
3.
Robert Gilmer 《Proceedings of the American Mathematical Society》2003,131(8):2337-2346
Let be an integral domain with quotient field and integral closure . An overring of is a subring of containing , and denotes the set of overrings of . We consider primarily two finiteness conditions on : (FO), which states that is finite, and (FC), the condition that each chain of distinct elements of is finite. (FO) is strictly stronger than (FC), but if , each of (FO) and (FC) is equivalent to the condition that is a Prüfer domain with finite prime spectrum. In general satisfies (FC) iff satisfies (FC) and all chains of subrings of containing have finite length. The corresponding statement for (FO) is also valid.
4.
Richard Delaware 《Proceedings of the American Mathematical Society》2003,131(8):2537-2542
A set is -straight if has finite Hausdorff -measure equal to its Hausdorff -content, where is continuous and non-decreasing with . Here, if satisfies the standard doubling condition, then every set of finite Hausdorff -measure in is shown to be a countable union of -straight sets. This also settles a conjecture of Foran that when , every set of finite -measure is a countable union of -straight sets.
5.
K. Tanahashi A. Uchiyama M. Uchiyama 《Proceedings of the American Mathematical Society》2003,131(8):2549-2552
We show Schwarz type inequalities and consider their converses. A continuous function is said to be semi-operator monotone on if is operator monotone on . Let be a bounded linear operator on a complex Hilbert space and be the polar decomposition of . Let and for . (1) If a non-zero function is semi-operator monotone on , then for , where . (2) If are semi-operator monotone on , then for . Also, we show converses of these inequalities, which imply that semi-operator monotonicity is necessary.
6.
Takahiko Nakazi 《Proceedings of the American Mathematical Society》2003,131(4):1267-1271
and denote the Hardy spaces on the open unit disc . Let be a function in and . If is an inner function and , then is orthogonal in . W.Rudin asked if the converse is true and C. Sundberg and C. Bishop showed that the converse is not true. Therefore there exists a function such that is not an inner function and is orthogonal in . In this paper, the following is shown: is orthogonal in if and only if there exists a unique probability measure on [0,1] with supp such that for nearly all in where is the Nevanlinna counting function of . If is an inner function, then is a Dirac measure at .
7.
Udayan B. Darji Tamá s Keleti 《Proceedings of the American Mathematical Society》2003,131(8):2593-2596
Motivated by a question of Gruenhage, we investigate when is the union of less than continuum many translates of a compact set . It will follow from one of our general results that if a compact set has packing dimension less than 1, then is not the union of less than continuum many translates of .
8.
Ahmad El Soufi Saï d Ilias 《Proceedings of the American Mathematical Society》2003,131(5):1611-1618
Let be a compact manifold. First, we give necessary and sufficient conditions for a Riemannian metric on to be extremal for with respect to conformal deformations of fixed volume. In particular, these conditions show that for any lattice of , the flat metric induced on from the standard metric of is extremal (in the previous sense). In the second part, we give, for any , an upper bound of on the conformal class of and exhibit a class of lattices for which the metric maximizes on its conformal class.
9.
Ana Meda 《Proceedings of the American Mathematical Society》2003,131(8):2597-2609
Let be a separable Banach space. Let be centered i.i.d. random vectors taking values on with law , , and let Under suitable conditions it is shown for every open and convex set that \varepsilon \Big\vert\frac{{\displaystyle S_n}}{\displaystyle n}\in D\right)$"> converges to zero (exponentially), where is the dominating point of As applications we give a different conditional weak law of large numbers, and prove a limiting aposteriori structure to a specific Gibbs twisted measure (in the direction determined solely by the same dominating point).
10.
On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces 总被引:3,自引:0,他引:3
Tomonari Suzuki 《Proceedings of the American Mathematical Society》2003,131(7):2133-2136
In this paper, we prove the following strong convergence theorem: Let be a closed convex subset of a Hilbert space . Let be a strongly continuous semigroup of nonexpansive mappings on such that . Let and be sequences of real numbers satisfying , 0$"> and . Fix and define a sequence in by for . Then converges strongly to the element of nearest to .
11.
Surjit Singh Khurana 《Proceedings of the American Mathematical Society》2003,131(3):937-939
Let be a completely regular Hausdorff space, a positive, finite Baire measure on , and a separable metrizable locally convex space. Suppose is a measurable mapping. Then there exists a sequence of functions in which converges to a.e. . If the function is assumed to be weakly continuous and the measure is assumed to be -smooth, then a separability condition is not needed.
12.
Davar Khoshnevisan Yimin Xiao 《Proceedings of the American Mathematical Society》2003,131(8):2611-2616
A probability measure on is called weakly unimodal if there exists a constant such that for all 0$">,
Here, denotes the -ball centered at with radius 0$">.
(0.1) |
Here, denotes the -ball centered at with radius 0$">.
In this note, we derive a sufficient condition for weak unimodality of a measure on the Borel subsets of . In particular, we use this to prove that every symmetric infinitely divisible distribution is weakly unimodal. This result is then applied to improve some recent results of the authors on capacities and level sets of additive Lévy processes.
13.
Saharon Shelah 《Proceedings of the American Mathematical Society》2003,131(8):2585-2592
If If is strongly compact and \kappa $"> and is regular (or alternatively cf , then holds for .
14.
Pham Anh Minh 《Proceedings of the American Mathematical Society》2003,131(2):363-368
Let be an odd prime number. The purpose of this paper is to provide a -group whose mod- cohomology ring has a nilpotent element satisfying .
15.
Jingbo Xia 《Proceedings of the American Mathematical Society》2003,131(8):2505-2514
For an analytic function which maps the open unit disc to itself, let be the operator of composition with on the Bergman space . It has been a longstanding problem to determine whether or not the membership of in the Schatten class , , is equivalent to the condition that the function has a finite integral with respect to the Möbius-invariant measure on . We show that the answer is negative when .
16.
In this note we provide an example of a semi-hyponormal Hilbert space operator for which is not -hyponormal for some and all .
17.
It is shown that the span of , where is the Haar system in and the canonical basis of , is well isomorphic to a well complemented subspace of . As a consequence we get that there is a rearrangement of the (initial segments of the) Haar system in , any block basis of which is well isomorphic to a well complemented subspace of .
18.
Leslie J. Bunce Antonio M. Peralta 《Proceedings of the American Mathematical Society》2003,131(4):1251-1255
A Banach space is said to have the alternative Dunford-Pettis property if, whenever a sequence weakly in with , we have for each weakly null sequence in X. We show that a -algebra has the alternative Dunford-Pettis property if and only if every one of its irreducible representations is finite dimensional so that, for -algebras, the alternative and the usual Dunford-Pettis properties coincide as was conjectured by Freedman. We further show that the predual of a von Neumann algebra has the alternative Dunford-Pettis property if and only if the von Neumann algebra is of type I.
19.
The automorphism group of a free group acts on the set of generating -tuples of a group . Higman showed that when , the union of conjugacy classes of the commutators and is an orbit invariant. We give a negative answer to a question of B.H. Neumann, as to whether there is a generalization of Higman's result for .
20.
Hans Schoutens 《Proceedings of the American Mathematical Society》2003,131(1):103-112
Using a tight closure argument in characteristic and then lifting the argument to characteristic zero with the aid of ultraproducts, I present an elementary proof of the Briançon-Skoda Theorem: for an -generated ideal of , the -th power of its integral closure is contained in . It is well-known that as a corollary, one gets a solution to the following classical problem. Let be a convergent power series in variables over which vanishes at the origin. Then lies in the ideal generated by the partial derivatives of .