共查询到20条相似文献,搜索用时 31 毫秒
1.
H. P. Goeters W. J. Wickless 《Proceedings of the American Mathematical Society》1998,126(11):3145-3150
A torsion-free abelian group is if every map from a pure subgroup of into lifts to an endomorphism of The class of groups has been extensively studied, resulting in a number of nice characterizations. We obtain some characterizations for the class of homogeneous groups, those homogeneous groups such that, for pure in every has a lifting to a quasi-endomorphism of An irreducible group is if and only if every pure subgroup of each of its strongly indecomposable quasi-summands is strongly indecomposable. A group is if and only if every endomorphism of is an integral multiple of an automorphism. A group has minimal test for quasi-equivalence ( if whenever and are quasi-isomorphic pure subgroups of then and are equivalent via a quasi-automorphism of For homogeneous groups, we show that in almost all cases the and properties coincide.
2.
Marjan Matvejchuk 《Proceedings of the American Mathematical Society》1998,126(4):1155-1164
Let be a real -algebra of -real bounded operators containing no central summand of type in a complex Hilbert space with conjugation . Denote by the quantum logic of all -orthogonal projections in the von Neumann algebra . Let be a probability measure. It is shown that contains a finite central summand and there exists a normal finite trace on such that , .
3.
Eve Oja 《Proceedings of the American Mathematical Society》1998,126(9):2747-2753
We prove that the space of compact operators on a Banach space is an -ideal in the space of bounded operators if and only if has the metric compact approximation property (MCAP), and is an -ideal in for all separable subspaces of having the MCAP. It follows that the Kalton-Werner theorem characterizing -ideals of compact operators on separable Banach spaces is also valid for non-separable spaces: for a Banach space is an -ideal in if and only if has the MCAP, contains no subspace isomorphic to and has property It also follows that is an -ideal in for all Banach spaces if and only if has the MCAP, and is an -ideal in .
4.
Stephen J. Gardiner 《Proceedings of the American Mathematical Society》1998,126(9):2699-2703
Let be open and be a bounded set which is closed relative to . We characterize those pairs such that, for each harmonic function on which is uniformly continuous on , there is a sequence of harmonic polynomials which converges to uniformly on . As an immediate corollary we obtain a characterization of Mergelyan pairs for harmonic functions.
5.
Aner Shalev 《Proceedings of the American Mathematical Society》1998,126(12):3495-3499
Let be a residually finite torsion group. We show that, if has a finite 2-subgroup whose centralizer is finite, then is locally finite. We also show that, if has no -torsion, and is a finite 2-group acting on in such a way that the centralizer is soluble, or of finite exponent, then is locally finite.
6.
Phan H. Loi 《Proceedings of the American Mathematical Society》1998,126(9):2651-2662
Given an irreducible inclusion of factors with finite index , where is of type , of type , , and are relatively prime positive integers, we will prove that if satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with . Relations between and a certain -kernel on subfactors are also discussed.
7.
Jutta Hausen Phillip Schultz 《Proceedings of the American Mathematical Society》1998,126(9):2525-2533
Let be a prime number and let be an abelian -group. Let be the maximal normal -subgroup of and the maximal -subgroup of its centre. Let be the torsion radical of . Then . The result is new for and 3, and the proof is new and valid for all primes .
8.
D. M. Speegle 《Proceedings of the American Mathematical Society》1998,126(12):3633-3637
If is an infinite dimensional, separable, uniformly smooth Banach space, then there is an , a Banach space containing as a closed subspace and a norm one map from to a space which does not extend to an operator from to with .
9.
K. S. Kazarian Robert E. Zink 《Proceedings of the American Mathematical Society》1998,126(10):2883-2893
We show that if is a subsystem of the Faber-Schauder system, and if is complete in , then is a quasibasis for each space , . Although it follows from the work of Ul'yanov that each element of can be represented by a Schauder series that converges unconditionally to the function, in the metric of the space, it proves to be the case that none of the aforementioned systems is an unconditional quasibasis for any of the -spaces herein considered.
10.
Paul Hill 《Proceedings of the American Mathematical Society》1998,126(11):3133-3135
We answer questions raised by P. Danchev in a recent paper in these Proceedings. It is shown that a -summable abelian -group is not determined by its socle, that is, two such groups can have isometric socles without being isomorphic. It is also demonstrated that -summability plays essentially no role in regard to the question of whether or not is totally projective, where denotes the group of normalized units of the group algebra with being a perfect field of characteristic .
11.
Tianxuan Miao 《Proceedings of the American Mathematical Society》1998,126(12):3571-3579
Let be a -compact locally compact nondiscrete group and let be a -invariant ideal of . We denote the set of left invariant means on that are zero on (i.e. for all ) by . We show that, when is amenable as a discrete group and the closed -invariant subset of the spectrum of corresponding to is a -set, is very large in the sense that every nonempty -subset of contains a norm discrete copy of , where is the Stone- compactification of the set of positive integers with the discrete topology. In particular, we prove that has no exposed points in this case and every nonempty -subset of the set of left invariant means on contains a norm discrete copy of .
12.
Abdelbaki Boutabaa Alain Escassut 《Proceedings of the American Mathematical Society》1998,126(9):2557-2568
Let be a complete ultrametric algebraically closed field of characteristic zero, and let be the field of meromorphic functions in . For all set in and for all we denote by the subset of : zero of order After studying unique range sets for entire functions in in a previous article, here we consider a similar problem for meromorphic functions by showing, in particular, that, for every , there exist sets of elements in such that, if have the same poles (counting multiplicities), and satisfy , then . We show how to construct such sets.
13.
14.
San Ling 《Proceedings of the American Mathematical Society》1998,126(11):3201-3210
For an integer and a prime not dividing , we study the kernel of the degeneracy map , where and are the component groups of and , respectively. This is then used to determine the kernel of the degeneracy map when . We also compute the group structure of in some cases.
15.
Eberhard Kaniuth Gitta Kutyniok 《Proceedings of the American Mathematical Society》1998,126(12):3561-3569
Let be a locally compact abelian group. The notion of Zak transform on extends to . Suppose that is compactly generated and its connected component of the identity is non-compact. Generalizing a classical result for , we then prove that if is such that its Zak transform is continuous on , then has a zero.
16.
Florin Pop 《Proceedings of the American Mathematical Society》1998,126(10):2987-2992
If is an inclusion of type factors with we study the connection between the existence of singular states on which extend the trace on and the Dixmier approximation property in with unitaries in We also prove the existence of singular conditional expectations from certain free product factors onto irreducible hyperfinite subfactors.
17.
Sultan Catto Jonathan Huntley Jay Jorgenson David Tepper 《Proceedings of the American Mathematical Society》1998,126(12):3455-3459
Let be the homogeneous space associated to the group
. Let where and consider the first nontrivial eigenvalue of the Laplacian on . Using geometric considerations, we prove the inequality . Since the continuous spectrum is represented by the band , our bound on can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.
. Let where and consider the first nontrivial eigenvalue of the Laplacian on . Using geometric considerations, we prove the inequality . Since the continuous spectrum is represented by the band , our bound on can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.
18.
Necessary and sufficient conditions for the optimality of a pair subject to are given. Here is a selfadjoint operator with closed range on a Hilbert space and . The case - unbounded is also discussed, which leads to some open problems. This general functional scheme includes most of the previous results on the optimal control of the -periodic wave equation for all in a dense subset of . It also includes optimal control problems for some elliptic equations.
19.
Let be a finite -solvable group for different primes and . Let and be such that . We prove that every of -degree has -degree if and only if and .
20.
A set of integers is said to be Glasner if for every infinite subset of the torus and there exists some such that the dilation intersects every integral of length in . In this paper we show that if denotes the th prime integer and is any non-constant polynomial mapping the natural numbers to themselves, then is Glasner. The theorem is proved in a quantitative form and generalizes a result of Alon and Peres (1992).