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1.
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 .
2.
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 .
3.
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.
4.
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 .
5.
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.
6.
Katsuyuki Yoshikawa 《Proceedings of the American Mathematical Society》1998,126(12):3727-3731
We consider the order of a meridian (of the group) of a Klein bottle smoothly embedded in the -sphere . The order of a meridian of a Klein bottle in is a non-negative even integer. Conversely, we prove that, for every non-negative even integer , there exists a Klein bottle in whose meridian has order .
7.
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.
8.
Assume and is a Lipschitz -mapping; and denote the volume and the surface area of . We verify that there exists a figure with , and, of course, , where depends only on the dimension and on . We also give an example when is a square and ; in fact, the boundary of can contain a fractal of Hausdorff dimension exceeding one.
9.
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 .
10.
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.
11.
On complementary subspaces of Hilbert space 总被引:1,自引:0,他引:1
W. E. Longstaff Oreste Panaia 《Proceedings of the American Mathematical Society》1998,126(10):3019-3026
Every pair of non-trivial topologically complementary subspaces of a Hilbert space is unitarily equivalent to a pair of the form on a Hilbert space . Here is possibly , is a positive injective contraction and denotes the graph of . For such a pair the following are equivalent: (i) is similar to a pair in generic position; (ii) and have a common algebraic complement; (iii) is similar to for some operators on a Hilbert space. These conditions need not be satisfied. A second example is given (the first due to T. Kato), involving only compact operators, of a double triangle subspace lattice which is not similar to any operator double triangle.
12.
John R. Stembridge 《Proceedings of the American Mathematical Society》1998,126(11):3177-3181
Let be a crystallographic reflection group with length function . We give a short and elementary derivation of the identity , where the product ranges over positive roots , and denotes the sum of the coordinates of with respect to the simple roots. We also prove that in the noncrystallographic case, this identity is valid in the limit ; i.e., .
13.
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.
14.
S. V. Kislyakov 《Proceedings of the American Mathematical Society》1998,126(11):3307-3314
For a positive function on the unit circle with , the following two statements are equivalent: (a) ; (b) there is an operator projecting onto for all at once and having weak type (1,1) with respect to .
15.
Chung-Wei Ha 《Proceedings of the American Mathematical Society》1998,126(12):3507-3511
We consider the eigenvalue problem in , , where keeps a fixed sign and , and we obtain some lower and upper bounds for in terms of its nonnegative eigenvalues . Two typical results are: (1) if and is not the square of a positive integer; (2) if is the smallest eigenvalue.
16.
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 .
17.
Mohammad S. R. Chowdhury Kok-Keong Tan 《Proceedings of the American Mathematical Society》1998,126(10):2957-2968
Let be a topological vector space and be a non-empty subset of . Let and be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point and a point such that for all . We shall use Chowdhury and Tan's 1996 generalized version of Ky Fan's minimax inequality as a tool to obtain some general theorems on solutions of the GQVI on a paracompact set in a Hausdorff locally convex space where the set-valued operator is either strongly pseudo-monotone or pseudo-monotone and is upper semicontinuous from to the weak-topology on for each non-empty finite subset of .
18.
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 .
19.
Yuuichi Suzuki Hajime Urakawa 《Proceedings of the American Mathematical Society》1998,126(10):3065-3069
We prove two first eigenvalue pinching theorems for Riemannian symmetric spaces (Theorems 1 and 2). As their application, we answer negatively a question raised by Elworthy and Rosenberg, who proposed to show that for every compact simple Lie group with a bi-invariant Riemannian metric on with respect to , being the Killing form of the Lie algebra , the first eigenvalue would satisfy
for all orthonormal bases of tangent spaces of (cf. Corollary 3). This problem arose in an attempt to give a spectral geometric proof that for a Lie group .
20.
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.