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1.
Katsuro Sakai 《Proceedings of the American Mathematical Society》1997,125(9):2809-2813
Let be the -dimensional universal Menger compactum, a -set in and a metrizable zero-dimensional compact group with the unit. It is proved that there exists a semi-free -action on such that is the fixed point set of every . As a corollary, it follows that each compactum with can be embedded in as the fixed point set of some semi-free -action on .
2.
Hypersurfaces in a sphere with constant mean curvature 总被引:13,自引:0,他引:13
Zhong Hua Hou 《Proceedings of the American Mathematical Society》1997,125(4):1193-1196
Let be a closed hypersurface of constant mean curvature immersed in the unit sphere . Denote by the square of the length of its second fundamental form. If , is a small hypersphere in . We also characterize all with .
3.
Changyu Xia 《Proceedings of the American Mathematical Society》1997,125(6):1801-1806
Let be an ()-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary . Assume that the principal curvatures of are bounded from below by a positive constant . In this paper, we prove that the first nonzero eigenvalue of the Laplacian of acting on functions on satisfies with equality holding if and only if is isometric to an -dimensional Euclidean ball of radius . Some related rigidity theorems for are also proved.
4.
Bilocal derivations of standard operator algebras 总被引:5,自引:0,他引:5
In this paper, we shall show the following two results: (1) Let be a standard operator algebra with , if is a linear mapping on which satisfies that maps into for all , then is of the form for some in . (2) Let be a Hilbert space, if is a norm-continuous linear mapping on which satisfies that maps into for all self-adjoint projection in , then is of the form for some in .
5.
Loukas Grafakos 《Proceedings of the American Mathematical Society》1997,125(11):3279-3288
We consider multilinear operators given by determinants of matrices of the form , where the 's are vector fields on . We give conditions on the 's so that the corresponding operator maps products of Lebesgue spaces into some anisotropic space , when .
6.
Jeffrey Bergen Piotr Grzeszczuk 《Proceedings of the American Mathematical Society》1997,125(12):3481-3488
If is an automorphism and is a -derivation of a ring , then the subring of invariants is the set The main result of this paper is Theorem. Let be a -derivation of an algebra over a commutative ring such that
for all , where and .
- (i)
- If , then .
- (ii)
- If is a -stable left ideal of such that , then .
7.
Sergey Dorofeev Klaus Thomsen 《Proceedings of the American Mathematical Society》1997,125(7):2007-2011
Let be an inclusion of -factors, the trace state of , and , the set of projections in and , respectively. We prove that the Jones index for the inclusion is
This formula is exploited to obtain continuity results for the index. In particular, we obtain a formula for the index which expresses in terms of the positions of and , in , when and are finite-dimensional -subalgebras with dense union in and , respectively.
8.
Athanassios G. Kartsatos 《Proceedings of the American Mathematical Society》1997,125(5):1469-1478
Let be a real, reflexive, locally uniformly convex Banach space with locally uniformly convex. Let be a maximal monotone operator and open and bounded. Assume that is pathwise connected and such that and Then If, moreover, is of type () on then may be replaced above by The significance of this result lies in the fact that it holds for multi-valued mappings which do not have to satisfy It has also been used in this paper in order to establish a general ``invariance of domain' result for maximal monotone operators, and may be applied to a greater variety of problems involving partial differential equations. No degree theory has been used. In addition to the above, necessary and sufficient conditions are given for the existence of a zero (in an open and bounded set ) of a completely continuous perturbation of a maximal monotone operator such that is locally monotone on
9.
Daniel M. Oberlin 《Proceedings of the American Mathematical Society》1997,125(5):1355-1361
Let and fix an interval . If is the operator on defined by , then maps into .
10.
Jø rgen Ellegaard Andersen 《Proceedings of the American Mathematical Society》1997,125(5):1511-1515
Let be a compact oriented surface with or without boundary components. In this note we prove that if then there exist infinitely many integers such that there is a point in the moduli space of irreducible flat connections on which is fixed by any orientation preserving diffeomorphism of . Secondly we prove that for each orientation preserving diffeomorphism of and each there is some such that has a fixed point in the moduli space of irreducible flat connections on . Thirdly we prove that for all there exists an integer such that the 'th power of any diffeomorphism fixes a certain point in the moduli space of irreducible flat connections on .
11.
Luis Paris 《Proceedings of the American Mathematical Society》1997,125(3):731-738
Let be a Coxeter system, and let be a subset of . The subgroup of generated by is denoted by and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the commensurator of in is the subgroup of in such that has finite index in both and . The subgroup can be decomposed in the form where is finite and all the irreducible components of are infinite. Let be the set of in such that for all . We prove that the commensurator of is . In particular, the commensurator of a parabolic subgroup is a parabolic subgroup, and is its own commensurator if and only if .
12.
Michael Rosen 《Proceedings of the American Mathematical Society》1997,125(5):1299-1303
Let be a finite field, , and . Let be the field extension of obtained by adjoining the -torsion on the Carlitz module. The class number of can be written as a product . The number is called the relative class number. In this paper a formula for is derived which is the analogue of the Maillet determinant formula for the relative class number of the cyclotomic field of -th roots of unity. Some consequences of this formula are also derived.
13.
Walter Feit 《Proceedings of the American Mathematical Society》1997,125(5):1259-1262
Let be a finite group with a faithful rational valued character of degree . A theorem of I. Schur gives a bound for the order of in terms of , generalizing an earlier result of H. Minkowski who showed that the same bound holds if . This note contains strengthened versions of these results which in particular show that a -subgroup of of maximum possible order contains a reflection.
14.
Ryszard Smarzewski 《Proceedings of the American Mathematical Society》1997,125(5):1391-1397
We give a new characterization of the set of all extreme points of the unit ball in the Banach space of all Lipschitz functions on a metric space This result is applied to get a total variation characterization of in the particular case when is a convex subset of a Banach space.
15.
Junxi Zhao 《Proceedings of the American Mathematical Society》1997,125(1):101-109
Let be a complete commutative subspace lattice on a Hilbert space. When is purely atomic, we give a necessary and sufficient condition for for every in , where and denote the spectrum of in and respectively. In addition, we discuss the properties of the spectra and the invertibility conditions for operators in .
16.
Teo Mora 《Proceedings of the American Mathematical Society》1997,125(5):1273-1282
It is proved for each , , that a primary -dimensional scheme in of degree in linearly general position lies in a rational normal scroll of dimension .
17.
Gennady Bachman 《Proceedings of the American Mathematical Society》1997,125(4):1001-1003
We evaluate , where the is taken over sequences satisfying . In particular we show that it is attained by taking for all , which reduces the summation over to a Ramanujan sum .
18.
Gennady Lyubeznik 《Proceedings of the American Mathematical Society》1997,125(7):1941-1944
We show that for fixed and the set of Bernstein-Sato polynomials of all the polynomials in at most variables of degrees at most is finite. As a corollary, we show that there exists an integer depending only on and such that generates as a module over the ring of the -linear differential operators of , where is an arbitrary field of characteristic 0, is the ring of polynomials in variables over and is an arbitrary non-zero polynomial of degree at most .
19.
Hiroaki Aikawa 《Proceedings of the American Mathematical Society》1997,125(1):229-234
Let be a bounded domain in , , and let . We consider positive functions on such that for all bounded harmonic functions on . We determine Lipschitz domains having such with .
20.
Marc Culler Peter B. Shalen 《Proceedings of the American Mathematical Society》1997,125(10):3059-3067
We show that if is a closed hyperbolic 3-manifold and if has a non-abelian free quotient, then the volume of is greater than . If, in addition, contains no genus- surface groups, then the volume of is greater than . Using these results we show that if there are infinitely many primitive homology classes in which are not represented by fibroids, then the volume of is greater than .