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1.
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 .
2.
A. Eduardo Gatto Stephen Vá gi 《Proceedings of the American Mathematical Society》1997,125(4):1149-1152
On a space of homogeneous type we consider functions in , , which are potentials of order of functions. We show that these functions belong to the class of smooth functions of Calderón-Scott. This result has applications to tangential convergence.
3.
Paul S. Bourdon 《Proceedings of the American Mathematical Society》1997,125(4):1187-1192
Let be a holomorphic function taking the open unit disk into itself. We show that the set of nonnegative powers of is orthogonal in if and only if the Nevanlinna counting function of , , is essentially radial. As a corollary, we obtain that the orthogonality of for a univalent implies for some constant . We also show that if is orthogonal, then the closure of must be a disk.
4.
On the von Neumann-Jordan constant for Banach spaces 总被引:2,自引:0,他引:2
Let be the von Neumann-Jordan constant for a Banach space . It is known that for any Banach space ; and is a Hilbert space if and only if . We show that: (i) If is uniformly convex, is less than two; and conversely the condition implies that admits an equivalent uniformly convex norm. Hence, denoting by the infimum of all von Neumann-Jordan constants for equivalent norms of , is super-reflexive if and only if . (ii) If , (the same value as that of -space), is of Rademacher type and cotype for any with , where ; the converse holds if is a Banach lattice and is finitely representable in or .
5.
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 .
6.
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 .
7.
A. Edward Nussbaum 《Proceedings of the American Mathematical Society》1997,125(12):3541-3545
Let and be semibounded (bounded from below) operators in a Hilbert space and a dense linear manifold contained in the domains of , , , and , and such that for all in . It is shown that if the restriction of to is essentially self-adjoint, then and are essentially self-adjoint and and commute, i.e. their spectral projections permute.
8.
Rings with finite essential socle 总被引:2,自引:0,他引:2
José L. Gó mez Pardo Pedro A. Guil Asensio 《Proceedings of the American Mathematical Society》1997,125(4):971-977
Let be a ring such that every direct summand of the injective envelope has an essential finitely generated projective submodule. We show that, if the cardinal of the set of isomorphism classes of simple right -modules is no larger than that of the isomorphism classes of minimal right ideals, then cogenerates the simple right -modules and has finite essential socle. This extends Osofsky's theorem which asserts that a right injective cogenerator ring has finite essential right socle. It follows from our result that if is a CS cogenerator, then is already an injective cogenerator and, more generally, that if is CS and cogenerates the simple right -modules, then it has finite essential socle. We show with an example that in the latter case need not be an injective cogenerator.
9.
Let be a reductive group and a parabolic subgroup. For every -regular dominant weight let denote the variety embedded in the projective space by the embedding corresponding to the ample line bundle . Writing , we prove that the degree of the dual variety to is a polynomial with nonnegative coefficients in . In the case of homogeneous spaces we find an expression for the constant term of this polynomial.
10.
Eric K. van Douwen David J. Lutzer 《Proceedings of the American Mathematical Society》1997,125(4):1237-1245
In this paper, we show that for generalized ordered spaces, paracompactness is equivalent to Property D, where a space is said to have Property D if, given any collection of open sets in satisfying for each , there is a closed discrete subset of satisfying .
11.
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.
12.
The purpose of this paper is to classify invariant hypercomplex structures on a -dimensional real Lie group . It is shown that the -dimensional simply connected Lie groups which admit invariant hypercomplex structures are the additive group of the quaternions, the multiplicative group of nonzero quaternions, the solvable Lie groups acting simply transitively on the real and complex hyperbolic spaces, and , respectively, and the semidirect product . We show that the spaces and possess an of (inequivalent) invariant hypercomplex structures while the remaining groups have only one, up to equivalence. Finally, the corresponding hyperhermitian -manifolds are determined.
13.
On perfect simple-injective rings 总被引:4,自引:0,他引:4
Harada calls a ring right simple-injective if every -homomorphism with simple image from a right ideal of to is given by left multiplication by an element of . In this paper we show that every left perfect, left and right simple-injective ring is quasi-Frobenius, extending a well known result of Osofsky on self-injective rings. It is also shown that if is left perfect and right simple-injective, then is quasi-Frobenius if and only if the second socle of is countably generated as a left -module, extending many recent results on self-injective rings. Examples are given to show that our results are non-trivial extensions of those on self-injective rings.
14.
James Cummings 《Proceedings of the American Mathematical Society》1997,125(9):2703-2709
Let be a singular cardinal in , and let be a model such that for some -cardinal with . We apply Shelah's pcf theory to study this situation, and prove the following results. 1) is not a -c.c generic extension of . 2) There is no ``good scale for ' in , so in particular weak forms of square must fail at . 3) If then and also . 4) If then .
15.
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 .
16.
For a locally convex Hausdorff topological vector space and for a system of weights vanishing at infinity on a locally compact Hausdorff space , let be the weighted space of -valued continuous functions on with the locally convex topology derived from the seminorms which are weighted analogues of the supremum norm. A characterization of the orthogonality preserving (Lamperti-type) operators on is presented in this paper.
17.
Robert C. Stolz 《Proceedings of the American Mathematical Society》1997,125(4):1215-1220
For each function that satisfies the law of large numbers with values in a certain class of locally convex spaces with the Radon-Nikodym property the following decomposition holds: , where is integrable by seminorm, and is a Pettis integrable function which is scalarly 0.
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.
Keiji Izuchi 《Proceedings of the American Mathematical Society》1997,125(4):1153-1159
Let be a sequence of bounded linear operators on such that and for every . It is proved that for every .
20.
Sadahiro Maeda Toshiaki Adachi 《Proceedings of the American Mathematical Society》1997,125(4):1197-1202
In a complex space form we shall investigate a smooth curve which is generated by a holomorphic Killing vector field on .