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1.
M. B. Bekka 《Proceedings of the American Mathematical Society》1998,126(2):507-514
The following results on uniqueness of invariant means are shown:
(i) Let be a connected almost simple algebraic group defined over . Assume that , the group of the real points in , is not compact. Let be a prime, and let be the compact -adic Lie group of the -points in . Then the normalized Haar measure on is the unique invariant mean on .
(ii) Let be a semisimple Lie group with finite centre and without compact factors, and let be a lattice in . Then integration against the -invariant probability measure on the homogeneous space is the unique -invariant mean on .
2.
Michael J. Puls 《Proceedings of the American Mathematical Society》1998,126(3):721-728
Let be a discrete group, the group ring of over and the Lebesgue space of with respect to Haar measure. It is known that if is torsion free elementary amenable, and , then . We will give a sufficient condition for this to be true when , and in the case we will give sufficient conditions for this to be false when .
3.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(3):647-652
Let be the finite field with elements and let denote the ring of polynomials in one variable with coefficients in . Let be a monic polynomial irreducible in . We obtain a bound for the least degree of a monic polynomial irreducible in ( odd) which is a quadratic non-residue modulo . We also find a bound for the least degree of a monic polynomial irreducible in which is a primitive root modulo .
4.
Christian Le Merdy 《Proceedings of the American Mathematical Society》1998,126(3):715-719
For any , let denote the classical -Schatten space of operators on the Hilbert space . It was shown by Varopoulos (for ) and by Blecher and the author (full result) that for any equipped with the Schur product is an operator algebra. Here we prove that (and thus for any ) is actually a -algebra, which means that it is isomorphic to some quotient of a uniform algebra in the Banach algebra sense.
5.
B. Shapiro 《Proceedings of the American Mathematical Society》1998,126(7):1923-1930
For a given real generic curve let denote the ruled hypersurface in consisting of all osculating subspaces to of codimension 2. In this note we show that for any two convex real projective curves and the pairs and are homeomorphic.
6.
A. Skopenkov 《Proceedings of the American Mathematical Society》1998,126(8):2467-2476
For a space let . Let act on and on by exchanging factors and antipodes respectively. We present a new short proof of the following theorem by Weber: For an -polyhedron and , if there exists an equivariant map , then is embeddable in . We also prove this theorem for a peanian continuum and . We prove that the theorem is not true for the 3-adic solenoid and .
7.
Mariusz Lemanczyk Sergey D. Sinel'shchikov 《Proceedings of the American Mathematical Society》1998,126(3):815-818
We show that for a class of type -cocycles over a -action of type its Mackey action must change the type.
8.
Nader Vakil 《Proceedings of the American Mathematical Society》1998,126(3):809-814
We introduce and study the notion of pseudo-uniform convergence which is a weaker variant of quasi-uniform convergence. Applications include the following nonstandard characterization of weak convergence. Let be an infinite set, the Banach space of all bounded real-valued functions on a bounded sequence in and Then the sequence converges weakly to if and only if the convergence is pointwise on and, for each strictly increasing function , each , and each , there is an unlimited such that .
9.
It is shown that the suspension order of the -fold cartesian product of real projective -space is less than or equal to the suspension order of the -fold symmetric product of and greater than or equal to , where and satisfy and . In particular has suspension order , and for fixed the suspension orders of the spaces are unbounded while their stable suspension orders are constant and equal to .
10.
Tadashi Yanai 《Proceedings of the American Mathematical Society》1998,126(8):2221-2228
In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let be a ring, its left Martindale quotient ring and a right ideal of having no nonzero left annihilator. (1) Let be a pointed coalgebra which measures such that the group-like elements of act as automorphisms of . If is prime and for , then . Furthermore, if the action of extends to and if such that , then . (2) Let be an endomorphism of given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If is semiprime and , then .
11.
Vicente Palmer 《Proceedings of the American Mathematical Society》1998,126(7):2089-2094
L. Karp and M. Pinsky proved that, for small radius , the mean exit time function of an extrinsic -ball in a hypersurface is bounded from below by the corresponding function defined on an extrinsic -ball in . A counterexample given by C. Mueller proves that this inequality doesn't holds in the large. In this paper we show that, if is convex, then the inequality holds for all radii. Moreover, we characterize the equality and show that analogous results are true in the sphere.
12.
A. Medrano P. Myers H. M. Stark A. Terras 《Proceedings of the American Mathematical Society》1998,126(3):701-710
We consider graphs attached to , where , for an odd prime , using an analogue of the Euclidean distance. These graphs are shown to be mostly non-Ramanujan, in contrast to the case of Euclidean graphs over finite fields.
13.
Farid Bahrami Henrik Shahgholian 《Proceedings of the American Mathematical Society》1998,126(3):745-750
For set , and let be a measure with compact support. Suppose, for , there are functions and (bounded) domains , both containing the support of with the property that in (weakly) and in the complement of . If in addition is convex, then and .
14.
Nguyen Tu Cuong 《Proceedings of the American Mathematical Society》1998,126(4):1017-1022
In this paper we give a notion of polynomial type of a Noetherian scheme and define the function by for all Then we show that if admits a dualizing complex and is equidimensional, is (lower) semicontinuous; moreover, in that case, the non-Cohen-Macaulay locus nCM is not Cohen-Macaulay} is biequidimensional iff is constant on nCM
15.
A. Matheson 《Proceedings of the American Mathematical Society》1998,126(7):2061-2063
A bounded composition operator on , where is the unit ball in , is Dunford-Pettis if and only if the radial limit function of takes values on the unit sphere only on a set of surface measure zero. A similar theorem holds on bounded strongly pseudoconvex domains with smooth boundary.
16.
Reinhold Hü bl Xiaotao Sun 《Proceedings of the American Mathematical Society》1998,126(7):1931-1940
If is a local Dedekind scheme and is a projective Cohen-Macaulay variety of relative dimension , then is torsionfree if and only if is arithmetically Cohen-Macaulay for a suitable embedding in . If is regular then is torsionfree whenever the multiplicity of the special fibre is not a multiple of the characteristic of the residue class field.
17.
Changsun Choi 《Proceedings of the American Mathematical Society》1998,126(4):1149-1153
We prove the weak-type inequality , , between a non-negative subharmonic function and an -valued smooth function , defined on an open set containing the closure of a bounded domain in a Euclidean space , satisfying , and , where is a constant. Here is the harmonic measure on with respect to 0. This inequality extends Burkholder's inequality in which and , a Euclidean space.
18.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(7):1955-1961
Let be a global function field, a degree one prime divisor of and let be the Dedekind domain of functions in regular outside . Let be the Hilbert class field of , the integral closure of in . Let be a rank one normalized Drinfeld -module and let be a prime ideal in . We explicitly determine the finite -module structure of . In particular, if , is an odd prime number and is the Carlitz -module, then the finite -module is always cyclic.
19.
If is a perfect field of characteristic , we show that the Quillen K-groups are uniquely -divisible for . In fact, the Milnor K-groups are uniquely -divisible for all . This implies that is -connected after profinite completion for a complete discrete valuation ring with perfect residue field.
20.
We determine the largest positive number with the property that whenever are endomorphisms, respectively unital isometries of the algebra of all bounded linear operators acting on a separable Hilbert space, holds for every nonzero and is surjective, then so is . It turns out that in the first case we have , while in the second one .