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1.
In this note it is shown that the metric is always Gromov hyperbolic, but that the metric is Gromov hyperbolic if and only if has exactly one boundary point. As a corollary we get a new proof for the fact that the quasihyperbolic metric is Gromov hyperbolic in uniform domains.
2.
Weimin Sheng 《Proceedings of the American Mathematical Society》2008,136(5):1795-1802
In most previous works on the existence of solutions to the -Yamabe problem, one assumes that the initial metric is -admissible. This is a pointwise condition. In this paper we prove that this condition can be replaced by a weaker integral condition.
3.
We prove that, in a locally integrable structure, the wave-front set of the trace of a CR function at a point in a totally real submanifold of maximal dimension is independent of the maximally real submanifold passing through the point .
4.
Masahiro Shioya 《Proceedings of the American Mathematical Society》2006,134(6):1819-1821
Let be a -supercompact cardinal. We show that carries a normal ultrafilter with a property introduced by Menas. With it we give a transparent proof of Kamo's theorem that carries a normal ultrafilter with the partition property.
5.
Dong Zhe 《Proceedings of the American Mathematical Society》2005,133(6):1629-1637
In this paper we prove that for any unital -weakly closed algebra which is -weakly generated by finite-rank operators in , every -weakly closed -submodule has . In the case of nest algebras, if are nests, we obtain the following -fold tensor product formula:
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
where each is the -weakly closed Alg -submodule determined by an order homomorphism from into itself.
6.
We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.
7.
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.
8.
Danny Calegari Nathan M. Dunfield 《Proceedings of the American Mathematical Society》2006,134(11):3131-3136
We give an example of a subgroup of which is a strictly ascending HNN extension of a non-abelian finitely generated free group . In particular, we exhibit a free group in of rank which is conjugate to a proper subgroup of itself. This answers positively a question of Drutu and Sapir (2005). The main ingredient in our construction is a specific finite volume (non-compact) hyperbolic 3-manifold which is a surface bundle over the circle. In particular, most of comes from the fundamental group of a surface fiber. A key feature of is that there is an element of in with an eigenvalue which is the square root of a rational integer. We also use the Bass-Serre tree of a field with a discrete valuation to show that the group we construct is actually free.
9.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Proceedings of the American Mathematical Society》2006,134(11):3319-3327
Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.
10.
11.
Shutao Chen Yunan Cui Henryk Hudzik 《Proceedings of the American Mathematical Society》2004,132(2):473-480
Criteria in order that an Orlicz space equipped with the Orlicz norm contains a linearly isometric copy (or an order linearly isometric copy) of (or ) are given.
12.
Antonio Aizpuru Francisco Javier Garcia-Pacheco 《Proceedings of the American Mathematical Society》2006,134(7):2109-2115
The aim of this paper is to study the set of all -summand vectors of a real Banach space . We provide a characterization of -summand vectors in smooth real Banach spaces and a general decomposition theorem which shows that every real Banach space can be decomposed as an -sum of a Hilbert space and a Banach space without nontrivial -summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces.
13.
Louis Jeanjean Kazunaga Tanaka 《Proceedings of the American Mathematical Society》2003,131(8):2399-2408
We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in :
where . Without the assumption of the monotonicity of , we show that the mountain pass value gives the least energy level.
where . Without the assumption of the monotonicity of , we show that the mountain pass value gives the least energy level.
14.
Theodore A. Slaman 《Proceedings of the American Mathematical Society》2004,132(8):2449-2456
Working in the base theory of , we show that for all , the bounding principle for -formulas ( ) is equivalent to the induction principle for -formulas ( ). This partially answers a question of J. Paris.
15.
Jack Sonn 《Proceedings of the American Mathematical Society》2008,136(6):1955-1960
Let be a monic polynomial in with no rational roots but with roots in for all , or equivalently, with roots mod for all . It is known that cannot be irreducible but can be a product of two or more irreducible polynomials, and that if is a product of irreducible polynomials, then its Galois group must be a union of conjugates of proper subgroups. We prove that for any , every finite solvable group that is a union of conjugates of proper subgroups (where all these conjugates have trivial intersection) occurs as the Galois group of such a polynomial, and that the same result (with ) holds for all Frobenius groups. It is also observed that every nonsolvable Frobenius group is realizable as the Galois group of a geometric, i.e. regular, extension of .
16.
Wolfgang Knirsch 《Mathematische Nachrichten》2004,265(1):15-23
On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
It is shown that continuous -local derivations on -algebras are derivations and surjective -local *-automorphisms on prime -algebras or on -algebras such that the identity element is properly infinite are *-automorphisms.
18.
Martha Alvarez Montserrat Corbera Joaquin Delgado Jaume Llibre 《Proceedings of the American Mathematical Society》2005,133(2):529-536
In the -body problem a central configuration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for and for 4$"> that if masses are located at fixed points in the plane, then there are only a finite number of ways to position the remaining th mass in such a way that they define a central configuration. Lindstrom leaves open the case . In this paper we prove the case using as variables the mutual distances between the particles.
19.
Douglas Cenzer André Nies 《Proceedings of the American Mathematical Society》2004,132(1):239-249
Let be the lattice of classes of reals. We show there are exactly two possible isomorphism types of end intervals, . Moreover, finiteness is first order definable in .
20.
M. Drissi M. El Hodaibi E. H. Zerouali 《Proceedings of the American Mathematical Society》2008,136(5):1609-1617
Let be a Banach space and let be the class that consists of all operators such that for every , the range of has a finite-codimension when it is closed. For an integer , we define the class as an extension of . We then study spectral properties of such operators, and we extend some known results of multi-cyclic operators with .