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1.
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 .
2.
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.
3.
Chen-bo Zhu 《Proceedings of the American Mathematical Society》1998,126(10):3125-3130
Let be the reductive dual pair . We show that if is a representation of (respectively ) obtained from duality correspondence with some representation of (respectively ), then its Gelfand-Kirillov dimension is less than or equal to
(respectively ).
(respectively ).
4.
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 .
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.
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 .
7.
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.
8.
Dong Myung Chung Tae Su Chung 《Proceedings of the American Mathematical Society》1998,126(8):2369-2376
Let be the space of test white noise functionals. We first introduce a family of products on including Wiener and Wick products, and then show that with each product , we can associate a first order differential operator, called a first order -differential operator. We next show that a first order -differential operator is indeed a continuous derivation under the product . We finally characterize by means of rotation-invariance and continuous derivation under the product . Here and are the Gross Laplacian and the number operator on , respectively.
9.
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 .
10.
Torben Maack Bisgaard 《Proceedings of the American Mathematical Society》1998,126(11):3227-3237
For a certain constant (a little less than ), every function satisfying , , is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence there is a positive definite matrix sequence which is not of positive type and which satisfies , . For a certain constant (a little greater than ), for every function satisfying , , there is a convolution semigroup of measures on , with moments of all orders, such that , , and for every such convolution semigroup the measure is Stieltjes indeterminate for all .
11.
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 .
12.
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 .
13.
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.
14.
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.
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.
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).
17.
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 .
18.
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.
19.
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 .
20.
Eiji Ogasa 《Proceedings of the American Mathematical Society》1998,126(10):3109-3116
Take transverse immersions such that (1) is an embedding, (2) and is connected, and (3) . Then we obtain three surface-links = (, ) in , where =(1,2,3), (2,3,1), (3,1,2). We prove that, we have the equality where is the Sato-Levine invariant of , if all are semi-boundary links.