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1.
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 .
2.
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 .
3.
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 .
4.
Toshihiro Okuyama Keiichi Watanabe 《Proceedings of the American Mathematical Society》1998,126(9):2631-2634
Let and be bounded linear operators, and let be a partial isometry on a Hilbert space. Suppose that (1) , (2) , (3) and (4) . Then we have .
5.
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.
6.
Let be factors generated by a periodic tower of finite dimensional -algebras. We prove that for sufficiently large , is -isomorphic to a subalgebra of .
7.
Tin-Yau Tam 《Proceedings of the American Mathematical Society》1998,126(9):2607-2614
Let be an Hermitian matrix with where are the ordered eigenvalues of . A result of Ky Fan (1949) asserts that if and are Hermitian matrices, then is majorized by . We extend the result in the framework of real semisimple Lie algebras in the following way. Let be a noncompact real semisimple Lie algebra with Cartan decomposition . We show that for any given , , where is the unique element corresponding to , in a fixed closed positive Weyl chamber of a maximal abelian subalgebra of in . Here the ordering is induced by the dual cone of . Fan's result corresponds to the Lie algebra . The compact case is also discussed. As applications, two unexpected singular values inequalities concerning the sum of two real matrices and the sum of two real skew symmetric matrices are obtained.
8.
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 .
9.
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 .
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.
Ralph Howard 《Proceedings of the American Mathematical Society》1998,126(9):2779-2787
Let be a complete two dimensional simply connected Riemannian manifold with Gaussian curvature . If is a compactly supported function of bounded variation on , then satisfies the Sobolev inequality
Conversely, letting be the characteristic function of a domain recovers the sharp form of the isoperimetric inequality for simply connected surfaces with . Therefore this is the Sobolev inequality ``equivalent' to the isoperimetric inequality for this class of surfaces. This is a special case of a result that gives the equivalence of more general isoperimetric inequalities and Sobolev inequalities on surfaces.
Under the same assumptions on , if is a closed curve and is the winding number of about , then the Sobolev inequality implies
which is an extension of the Banchoff-Pohl inequality to simply connected surfaces with curvature .
12.
S. Hassi H. S. V. de Snoo A. D. I. Willemsma 《Proceedings of the American Mathematical Society》1998,126(9):2663-2675
Let be a selfadjoint operator in a Hilbert space with inner product . The rank one perturbations of have the form , , for some element . In this paper we consider smooth perturbations, i.e. we consider for some . Function-theoretic properties of their so-called -functions and operator-theoretic consequences will be studied.
13.
Ferran Cedó Dolors Herbera 《Proceedings of the American Mathematical Society》1998,126(9):2541-2548
For each positive integer , we construct a commutative ring such that the polynomial ring satisfies the maximum condition on annihilators and does not. In particular, there exists a commutative Kerr ring such that is not Kerr. This answers in the negative a question of Faith's.
14.
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.
15.
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 .
16.
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.
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.
Global iteration schemes for strongly pseudo-contractive maps 总被引:7,自引:0,他引:7
C. E. Chidume 《Proceedings of the American Mathematical Society》1998,126(9):2641-2649
Suppose is a real uniformly smooth Banach space, is a nonempty closed convex and bounded subset of , and is a strong pseudo-contraction. It is proved that if has a fixed point in then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in , converge strongly to the unique fixed . No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.
19.
P. C. Kunstmann 《Proceedings of the American Mathematical Society》1998,126(9):2721-2724
Let be a Banach space and a strongly continuous semigroup with . We show that the generator of generates a regularized semigroup. Our construction of a regularizing operator uses an existence result of J. Esterle.
20.
Let be a finite irreducible complex linear group with -power degree, where is a prime number. Then every -subgroup of that is normalized by a Sylow -subgroup must be abelian. This and related results are proved using an elementary character-theoretic argument.