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1.
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 .
2.
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 .
3.
K. Alan Loper 《Proceedings of the American Mathematical Society》1998,126(3):657-660
Let be an integral domain with quotient field . The ring of integer-valued polynomials over is defined by . It is known that if is a Prüfer domain, then is an almost Dedekind domain with all residue fields finite. This condition is necessary and sufficient if is Noetherian, but has been shown to not be sufficient if is not Noetherian. Several authors have come close to a complete characterization by imposing bounds on orders of residue fields of and on normalized values of particular elements of . In this note we give a double-boundedness condition which provides a complete charaterization of all integral domains such that is a Prüfer domain.
4.
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 .
5.
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.
6.
Zuzana Kü hn Uwe Rö sler 《Proceedings of the American Mathematical Society》1998,126(3):769-777
Lyapunov proved that the range of finite measures defined on the same -algebra is compact, and if each measure also is atomless, then the range is convex. Although both conclusions may fail for measures on different -algebras of the same set, they do hold if the -algebras are nested, which is exactly the setting of classical optimal stopping theory.
7.
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 .
8.
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 .
9.
Let be a nonzero ordinal such that for every ordinal . A chain domain (i.e. a domain with linearly ordered lattices of left ideals and right ideals) is constructed such that is isomorphic with all its nonzero factor-rings and is the ordinal type of the set of proper ideals of . The construction provides answers to some open questions.
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.
Marí a C. Pereyra Lesley A. Ward 《Proceedings of the American Mathematical Society》1998,126(1):135-144
We analyze the stability of Muckenhoupt's and classes of weights under a nonlinear operation, the -operation. We prove that the dyadic doubling reverse Hölder classes are not preserved under the -operation, but the dyadic doubling classes are preserved for . We give an application to the structure of resolvent sets of dyadic paraproduct operators.
12.
Pawe l Kolwicz Ryszard Pluciennik 《Proceedings of the American Mathematical Society》1998,126(8):2315-2322
A characterization of -convexity of arbitrary Banach space is given. Moreover, it is proved that the Orlicz-Bochner function space is P-convex if and only if both spaces and are -convex. In particular, the Lebesgue-Bochner space with is -convex iff is -convex.
13.
Pá draig Kirwan Raymond A. Ryan 《Proceedings of the American Mathematical Society》1998,126(4):1023-1029
We study the -homogeneous polynomials on a Banach space that can be extended to any space containing . We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible -homogeneous polynomials on and we characterize the extendible 2-homogeneous polynomials on when is a Hilbert space, an -space or an -space.
14.
We prove that for an arbitrary chain of prime ideals in an integral domain, there exists a valuation domain which has a chain of prime ideals lying over .
15.
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.
16.
Humio Ichimura 《Proceedings of the American Mathematical Society》1998,126(5):1315-1320
For any totally real number field and any prime number , Greenberg's conjecture for asserts that the Iwasawa invariants and are both zero. For a fixed real abelian field , we prove that the conjecture is ``affirmative' for infinitely many (which split in if we assume the abc conjecture for .
17.
Fanwei Meng Jizhong Wang Zhaowen Zheng 《Proceedings of the American Mathematical Society》1998,126(2):391-395
Some oscillation criteria are given for the second order matrix differential system , where and are real continuous matrix functions with symmetric, . These results improve oscillation criteria recently discovered by Erbe, Kong and Ruan by using a generalized Riccati transformation , where is the identity matrix, is a given function on and .
18.
Peter B. Gilkey John V. Leahy Jeong Hyeong Park 《Proceedings of the American Mathematical Society》1998,126(6):1845-1850
Let be a Riemannian submersion of closed manifolds. Let be an eigen -form of the Laplacian on with eigenvalue which pulls back to an eigen -form of the Laplacian on with eigenvalue . We are interested in when the eigenvalue can change. We show that , so the eigenvalue can only increase; and we give some examples where , so the eigenvalue changes. If the horizontal distribution is integrable and if is simply connected, then , so the eigenvalue does not change.
19.
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.
20.
Joan Cerdà Joaquim Martí n 《Proceedings of the American Mathematical Society》1998,126(8):2341-2344
We prove that for a decreasing weight on , the conjugate Hardy transform is bounded on () if and only if it is bounded on the cone of all decreasing functions of . This property does not depend on .