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1.
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 .
2.
The boundary behavior of the Bergman metric near a convex boundary point of a pseudoconvex domain is studied. It turns out that the Bergman metric at points in the direction of a fixed vector tends to infinity, when is approaching , if and only if the boundary of does not contain any analytic disc through in the direction of .
3.
Thomas Schlumprecht Vladimir G. Troitsky 《Proceedings of the American Mathematical Society》2003,131(5):1405-1413
We show that C. J. Read's example of an operator on which does not have any non-trivial invariant subspaces is not the adjoint of an operator on a predual of . Furthermore, we present a bounded diagonal operator such that even though is unbounded, the operator is a bounded operator on with invariant subspaces, and is adjoint to an operator on .
4.
Wieslaw Kubis 《Proceedings of the American Mathematical Society》2003,131(2):619-623
A coloring of a set is any subset of , where 1$"> is a natural number. We give some sufficient conditions for the existence of a perfect -homogeneous set, in the case where is and is a Polish space. In particular, we show that it is sufficient that there exist -homogeneous sets of arbitrarily large countable Cantor-Bendixson rank. We apply our methods to show that an analytic subset of the plane contains a perfect -clique if it contains any uncountable -clique, where is a natural number or (a set is a -clique in if the convex hull of any of its -element subsets is not contained in ).
5.
Ahmad El Soufi Saï d Ilias 《Proceedings of the American Mathematical Society》2003,131(5):1611-1618
Let be a compact manifold. First, we give necessary and sufficient conditions for a Riemannian metric on to be extremal for with respect to conformal deformations of fixed volume. In particular, these conditions show that for any lattice of , the flat metric induced on from the standard metric of is extremal (in the previous sense). In the second part, we give, for any , an upper bound of on the conformal class of and exhibit a class of lattices for which the metric maximizes on its conformal class.
6.
Liana M. Sega 《Proceedings of the American Mathematical Society》2003,131(8):2313-2323
We prove that if , are finite modules over a Gorenstein local ring of codimension at most , then the vanishing of for is equivalent to the vanishing of for . Furthermore, if has no embedded deformation, then such vanishing occurs if and only if or has finite projective dimension.
7.
On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces 总被引:3,自引:0,他引:3
Tomonari Suzuki 《Proceedings of the American Mathematical Society》2003,131(7):2133-2136
In this paper, we prove the following strong convergence theorem: Let be a closed convex subset of a Hilbert space . Let be a strongly continuous semigroup of nonexpansive mappings on such that . Let and be sequences of real numbers satisfying , 0$"> and . Fix and define a sequence in by for . Then converges strongly to the element of nearest to .
8.
Felix Schlenk 《Proceedings of the American Mathematical Society》2003,131(6):1925-1929
We consider a connected smooth -dimensional manifold endowed with a volume form , and we show that an open subset of of Lebesgue measure embeds into by a smooth volume preserving embedding whenever the volume condition is met.
9.
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.
10.
Stephen J. Gardiner Mary Hanley 《Proceedings of the American Mathematical Society》2003,131(3):773-779
Let denote a relatively closed subset of the unit ball of . The purpose of this paper is to characterize those sets which have the following property: any harmonic function on which satisfies on (where 0$">) can be locally uniformly approximated on by a sequence of harmonic polynomials which satisfy the same inequality on . This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.
11.
Agnes T. Paras Lutz Strü ngmann 《Proceedings of the American Mathematical Society》2003,131(2):371-377
An abelian -group is called (fully) transitive if for all with ( ) there exists an automorphism (endomorphism) of which maps onto . It is a long-standing problem of A. L. S. Corner whether there exist non-transitive but fully transitive -groups with finite first Ulm subgroup. In this paper we restrict ourselves to -groups of type , this is to say -groups satisfying . We show that the answer to Corner's question is no if is finite and is of type .
12.
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.
13.
M. Cristina Costoya-Ramos 《Proceedings of the American Mathematical Society》2003,131(2):637-645
Soit un espace ayant le type d'homotopie rationnelle d'un produit de sphères impaires. Si, pour tout nombre premier , la LS-catégorie de tous les -localisés de est majorée par , nous montrons que la LS-catégorie de est majorée par . Si est un élément dans le genre de Mislin de , nous en déduisons: . Dans le cas d'un -espace de rang 2, nous avons exactement , pour tout espace dans le genre de .
14.
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.
15.
Karel Dekimpe 《Proceedings of the American Mathematical Society》2003,131(3):973-978
We are dealing with Lie groups which are diffeomorphic to , for some . After identifying with , the multiplication on can be seen as a map . We show that if is a polynomial map in one of the two (sets of) variables or , then is solvable. Moreover, if one knows that is polynomial in one of the variables, the group is nilpotent if and only if is polynomial in both its variables.
16.
Lars Kadison 《Proceedings of the American Mathematical Society》2003,131(10):2993-3002
Since an H-separable extension is of depth two, we associate to it dual bialgebroids and over the centralizer as in Kadison-Szlachányi. We show that has an antipode and is a Hopf algebroid. is also Hopf algebroid under the condition that the centralizer is an Azumaya algebra over the center of . For depth two extension , we show that .
17.
Ulrich Albrecht 《Proceedings of the American Mathematical Society》2003,131(4):1021-1029
This paper investigates the extent to which an Abelian group is determined by the homomorphism groups . A class of Abelian groups is a Fuchs 34 class if and in are isomorphic if and only if for all . Two -groups and satisfy for all groups if and only if they have the same -Ulm-Kaplansky-invariants and the same final rank. The mixed groups considered in this context are the adjusted cotorsion groups and the class introduced by Glaz and Wickless. While is a Fuchs 34 class, the class of (adjusted) cotorsion groups is not. 相似文献
18.
Larry Smith 《Proceedings of the American Mathematical Society》2003,131(4):1043-1048
Let be a representation of a finite group over the field . Denote by the algebra of polynomial functions on the vector space . The group acts on and hence also on . The algebra of coinvariants is , where is the ideal generated by all the homogeneous -invariant forms of strictly positive degree. If the field has characteristic zero, then R. Steinberg has shown (this is the formulation of R. Kane) that is a Poincaré duality algebra if and only if is a pseudoreflection group. In this note we explore the situation for fields of nonzero characteristic. We prove an analogue of Steinberg's theorem for the case and give a counterexample in the modular case when .
19.
Inhyeop Yi 《Proceedings of the American Mathematical Society》2003,131(4):1273-1282
Let be an edge-wrapping rule which presents a one-dimensional generalized solenoid , and let be the adjacency matrix of . When is a wedge of circles and leaves the unique branch point fixed, we show that the stationary dimension group of is an invariant of homeomorphism of even if is not orientable.