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1.
A. Chigogidze A. Karasev M. Rø rdam 《Proceedings of the American Mathematical Society》2004,132(3):783-788
It is proved that if is a compact Hausdorff space of Lebesgue dimension , then the squaring mapping , defined by , is open if and only if . Hence the Lebesgue dimension of can be detected from openness of the squaring maps . In the case it is proved that the map , from the selfadjoint elements of a unital -algebra into its positive elements, is open if and only if is isomorphic to for some compact Hausdorff space with .
2.
Flavio Abdenur Artur Avila Jairo Bochi 《Proceedings of the American Mathematical Society》2004,132(3):699-705
We prove that nontrivial homoclinic classes of -generic flows are topologically mixing. This implies that given , a nontrivial -robustly transitive set of a vector field , there is a -perturbation of such that the continuation of is a topologically mixing set for . In particular, robustly transitive flows become topologically mixing after -perturbations. These results generalize a theorem by Bowen on the basic sets of generic Axiom A flows. We also show that the set of flows whose nontrivial homoclinic classes are topologically mixing is not open and dense, in general.
3.
Pamela B. Pierce Daniel Waterman 《Proceedings of the American Mathematical Society》2004,132(3):755-760
The necessary and sufficient condition for to be in the class for every of that class whose range is in the domain of is that be in .
4.
Z. Ercan 《Proceedings of the American Mathematical Society》2004,132(6):1761-1763
We prove that for a compact Hausdorff space without isolated points, and are isometrically Riesz isomorphic spaces under a certain topology on . Moreover, is a closed subspace of . This provides concrete examples of compact Hausdorff spaces such that the Dedekind completion of is (= the set of all bounded real-valued functions on ) since the Dedekind completion of is ( and spaces as Banach lattices).
5.
John T. Anderson Alexander J. Izzo John Wermer 《Proceedings of the American Mathematical Society》2004,132(5):1495-1500
We prove: Let be a compact real-analytic variety in . Assume (i) is polynomially convex and (ii) every point of is a peak point for . Then . This generalizes a previous result of the authors on polynomial approximation on three-dimensional real-analytic submanifolds of .
6.
Teresa Crespo 《Proceedings of the American Mathematical Society》2004,132(3):691-695
We present an explicit construction of the complete family of Galois extensions of a field of characteristic 3 with Galois group the central product of a double cover of the symmetric group and the quaternion group , containing a given -extension of the field .
7.
A. S. Kleshchev A. E. Zalesski 《Proceedings of the American Mathematical Society》2004,132(6):1605-1612
Let be an algebraically closed field of characteristic 0$"> and let be a quasi-simple group with . We describe the minimal polynomials of elements of order in irreducible representations of over . If , we determine the minimal polynomials of elements of order in -modular irreducible representations of , , , , , and .
8.
Malkhaz Bakuradze Stewart Priddy 《Proceedings of the American Mathematical Society》2004,132(6):1855-1860
Let be a complex -plane bundle over the total space of a cyclic covering of prime index . We show that for the -th Chern class of the transferred bundle differs from a certain transferred class of by a polynomial in the Chern classes of the transferred bundle. The polynomials are defined by the formal group law and certain equalities in .
9.
Martin Mathieu 《Proceedings of the American Mathematical Society》2004,132(2):443-446
A linear mapping from a subspace of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant such that for all , where denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple -algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.
10.
Let be a complex Hilbert space, be the algebra of all bounded linear operators on , be the subset of all selfadjoint operators in and or . Denote by the numerical radius of . We characterize surjective maps that satisfy for all without the linearity assumption.
11.
For we give examples of Banach spaces isometrically embedding into but not into any with
12.
Chun-Gil Park 《Proceedings of the American Mathematical Society》2004,132(6):1739-1745
It is shown that for an approximate algebra homomorphism on a Banach -algebra , there exists a unique algebra -homomorphism near the approximate algebra homomorphism. This is applied to show that for an approximate automorphism on a unital -algebra , there exists a unique automorphism near the approximate automorphism. In fact, we show that the approximate automorphism is an automorphism.
13.
In this paper, we investigate the Hansen-Mullen conjecture with the help of some formal series similar to the Artin-Hasse exponential series over -adic number fields and the estimates of character sums over Galois rings. Given we prove, for large enough , the Hansen-Mullen conjecture that there exists a primitive polynomial over of degree with the -th ( coefficient fixed in advance except when if is odd and when if is even.
14.
Nobushige Kurokawa Masato Wakayama 《Proceedings of the American Mathematical Society》2004,132(4):935-943
We introduce and study a -analogue of the Euler constant via a suitably defined -analogue of the Riemann zeta function. We show, in particular, that the value is irrational. We also present a -analogue of the Hurwitz zeta function and establish an analogue of the limit formula of Lerch in 1894 for the gamma function. This limit formula can be regarded as a natural generalization of the formula of .
15.
W. K. Ziemer 《Proceedings of the American Mathematical Society》2004,132(7):1987-1995
It is shown that a -cell (the homeomorphic image of a closed ball in ) in , , cannot support a function in if [\frac{k+1}{2}]$">, the greatest integer in .
16.
Alexandre Turull 《Proceedings of the American Mathematical Society》2004,132(9):2563-2565
We observe a simple formula to compute the number of Hall -subgroups of a -separable finite group in terms of only the action of a fixed Hall -subgroup of on a set of normal -sections of . As a consequence, we obtain that divides whenever is a subgroup of a finite -separable group . This generalizes a recent result of Navarro. In addition, our method gives an alternative proof of Navarro's result.
17.
Qingying Bu 《Proceedings of the American Mathematical Society》2004,132(2):381-384
D. R. Lewis (1977) proved that for a Banach space and , , the projective tensor product of and , is weakly sequentially complete whenever is weakly sequentially complete. In this note, we give a short proof of Lewis's result, based on our sequential representation (2001) of .
18.
Jan Jaworowski 《Proceedings of the American Mathematical Society》2004,132(4):1223-1228
Suppose that is a vector bundle with a linear periodic map of period ; the map is assumed free on the outside of the -section. A polynomial , called a mod Chern polynomial of , is defined. It is analogous to the Stiefel-Whitney polynomial defined by Dold for real vector bundles with the antipodal involution. The mod Chern polynomial can be used to measure the size of the periodic coincidence set for fibre preserving maps of the unit sphere bundle of into another vector bundle.
19.
In this note, we show that one can derive from any -spline function of order ( ) an MRA tight wavelet frame in that is generated by the dyadic dilates and integer shifts of three compactly supported real-valued symmetric wavelet functions with vanishing moments of the highest possible order .
20.
Douglas Cenzer André Nies 《Proceedings of the American Mathematical Society》2004,132(1):239-249
Let be the lattice of classes of reals. We show there are exactly two possible isomorphism types of end intervals, . Moreover, finiteness is first order definable in .