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1.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》1998,126(12):3545-3547
Let be a symmetric Banach -algebra, let be a Banach algebra, and assume that . A result is proved giving conditions which imply that every element of has the same spectrum in both and .
2.
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 .
3.
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.
4.
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.
5.
Sufficient conditions for one domain to contain another in a space of constant curvature 总被引:4,自引:0,他引:4
Jiazu Zhou 《Proceedings of the American Mathematical Society》1998,126(9):2797-2803
As an application of the analogue of C-S. Chen's kinematic formula in the 3-dimensional space of constant curvature , that is, Euclidean space , -sphere , hyperbolic space (, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space , or a -sphere or a hyperbolic space .
6.
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.
7.
Michel Brion 《Proceedings of the American Mathematical Society》1998,126(9):2535-2539
Let be a smooth affine algebraic variety where a reductive algebraic group acts with a smooth quotient space . We show that the algebraic differential forms on which are pull-backs of forms on are exactly the -invariant horizontal differential forms on .
8.
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.
9.
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.
10.
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.
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.
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 .
13.
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 .
14.
R. N. Cruz K. A. de Rezende 《Proceedings of the American Mathematical Society》1998,126(12):3715-3720
We show that the cycle-rank of a Lyapunov graph on a manifold satisfies: , where is the genus of . This generalizes a theorem of Franks. We also show that given any integer with , for some Lyapunov graph on .
15.
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 .
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17.
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 .
18.
Ivica Gusic 《Proceedings of the American Mathematical Society》1998,126(9):2593-2597
We show that a lattice ordered group can be topologized in a natural way. The topology depends on the choice of a set of admissible elements (-topology). If a lattice ordered group is 2-divisible and satisfies a version of Archimedes' axiom (-group), then we show that the -topology is Hausdorff. Moreover, we show that a -group with the -topology is a topological group.
19.
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.
20.
M. I. Berenguer A. R. Villena 《Proceedings of the American Mathematical Society》1998,126(9):2717-2720
Let and be centrally closed prime complex Banach algebras with linear involution. If is semisimple, then any Lie derivation of the skew elements of is continuous and any Lie isomorphism from the skew elements of onto the skew elements of is continuous.