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1.
Y. Bahturin A. Giambruno M. Zaicev 《Proceedings of the American Mathematical Society》1999,127(1):63-69
Let be an algebra over a field and a finite group of automorphisms and anti-automorphisms of . We prove that if satisfies an essential -polynomial identity of degree , then the -codimensions of are exponentially bounded and satisfies a polynomial identity whose degree is bounded by an explicit function of . As a consequence we show that if is an algebra with involution satisfying a -polynomial identity of degree , then the -codimensions of are exponentially bounded; this gives a new proof of a theorem of Amitsur stating that in this case must satisfy a polynomial identity and we can now give an upper bound on the degree of this identity.
2.
Marco Bramanti Luca Brandolini 《Transactions of the American Mathematical Society》2000,352(2):781-822
Let be a system of real smooth vector fields, satisfying Hörmander's condition in some bounded domain (). We consider the differential operator
where the coefficients are real valued, bounded measurable functions, satisfying the uniform ellipticity condition:
for a.e. , every , some constant . Moreover, we assume that the coefficients belong to the space VMO (``Vanishing Mean Oscillation'), defined with respect to the subelliptic metric induced by the vector fields . We prove the following local -estimate:
for every , . We also prove the local Hölder continuity for solutions to for any with large enough. Finally, we prove -estimates for higher order derivatives of , whenever and the coefficients are more regular.
3.
Mingliang Cai 《Proceedings of the American Mathematical Society》1999,127(2):569-575
We prove some integral inequalities for immersed tori in the three sphere. The functionals considered are generalizations of the Willmore functional.
4.
Hiroshi Koshimizu Kiyoshi Takeuchi 《Proceedings of the American Mathematical Society》2000,128(6):1685-1690
Some extension theorems for the distribution solutions to - modules will be given. We will use the notion of regular singularities introduced by Kashiwara-Oshima (1977).
5.
Juraj Simko 《Proceedings of the American Mathematical Society》1999,127(2):323-325
It is proved that the theory of the class of all betweenness spaces metrizable by real-valued metrics does not coincide with the theory of the class of all betweenness spaces metrizable by metrics taking values in any ordered field. This solves a problem raised by Mendris and Zlatov{s}.
6.
L. Rodrí guez-Piazza M. C. Romero-Moreno 《Transactions of the American Mathematical Society》2000,352(1):379-395
Let be a real number such that and its conjugate exponent . We prove that for an operator defined on with values in a Banach space, the image of the unit ball determines whether belongs to any operator ideal and its operator ideal norm. We also show that this result fails to be true in the remaining cases of . Finally we prove that when the result holds in finite dimension, the map which associates to the image of the unit ball the operator ideal norm is continuous with respect to the Hausdorff metric.
7.
Christopher Hoffman 《Transactions of the American Mathematical Society》1999,351(10):4263-4280
We present a general method for constructing families of measure preserving transformations which are and loosely Bernoulli with various ergodic theoretical properties. For example, we construct two transformations which are weakly isomorphic but not isomorphic, and a transformation with no roots. Ornstein's isomorphism theorem says families of Bernoulli shifts cannot have these properties. The construction uses a combination of properties from maps constructed by Ornstein and Shields, and Rudolph, and reduces the question of isomorphism of two transformations to the conjugacy of two related permutations.
8.
T. S. Quek 《Proceedings of the American Mathematical Society》1999,127(8):2343-2351
In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type on if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery's result is sharp in a certain sense. We also obtain a weighted analogue of Carbery's result. Some applications of our results are also given.
9.
Jen-Tseh Chang James W. Cogdell 《Proceedings of the American Mathematical Society》1999,127(4):1251-1256
We compute the -homology for a class of representations of
and which admit a Whittaker model. They are all completely reducible.
and which admit a Whittaker model. They are all completely reducible.
10.
Anthony Bahri Martin Bendersky 《Transactions of the American Mathematical Society》2000,352(3):1191-1202
Toric manifolds, a topological generalization of smooth projective toric varieties, are determined by an -dimensional simple convex polytope and a function from the set of codimension-one faces into the primitive vectors of an integer lattice. Their cohomology was determined by Davis and Januszkiewicz in 1991 and corresponds with the theorem of Danilov-Jurkiewicz in the toric variety case. Recently it has been shown by Buchstaber and Ray that they generate the complex cobordism ring. We use the Adams spectral sequence to compute the -theory of all toric manifolds and certain singular toric varieties.
11.
Neal J. Fowler Marcelo Laca Iain Raeburn 《Proceedings of the American Mathematical Society》2000,128(8):2319-2327
We associate -algebras to infinite directed graphs that are not necessarily locally finite. By realizing these algebras as Cuntz-Krieger algebras in the sense of Exel and Laca, we are able to give criteria for their uniqueness and simplicity, generalizing results of Kumjian, Pask, Raeburn, and Renault for locally finite directed graphs.
12.
Byeong-Kweon Oh 《Proceedings of the American Mathematical Society》2000,128(3):683-689
Let be the minimal rank of -universal -lattices, by which we mean positive definite -lattices which represent all positive -lattices of rank . It is a well known fact that for . In this paper, we determine and find all -universal lattices of rank for .
13.
Robert Lauter 《Proceedings of the American Mathematical Society》2000,128(7):1955-1961
We compute the length of the -algebra generated by the algebra of b-pseudodifferential operators of order on compact manifolds with corners.
14.
15.
Suppose is a simple reductive -adic group with Weyl group . We give a classification of the irreducible representations of which can be extended to real hermitian representations of the associated graded Hecke algebra . Such representations correspond to unitary representations of which have a small spectrum when restricted to an Iwahori subgroup.
16.
Let , be -algebras and a full Hilbert --bimodule such that every closed right submodule is orthogonally closed, i.e., . Then there are families of Hilbert spaces , such that and are isomorphic to -direct sums , resp. , and is isomorphic to the outer direct sum .
17.
Tejinder Neelon 《Proceedings of the American Mathematical Society》1999,127(7):2099-2104
It is well known that a function whose restriction to every line in is real analytic must itself be real analytic. In this note we study whether this property of real analytic functions is also possessed by some other subclasses of functions. We prove that if is ultradifferentiable corresponding to a sequence on every line in some `uniform way', then is ultradifferentiable corresponding to the sequence
18.
Michael Levin James T. Rogers Jr. 《Proceedings of the American Mathematical Society》2000,128(5):1537-1541
We prove that if an open map of compacta and has perfect fibers and is a -space, then there exists a -dimensional compact subset of intersecting each fiber of . This is a stronger version of a well-known theorem of Kelley. Applications of this result and related topics are discussed.
19.
Pierre Dusart. 《Mathematics of Computation》1999,68(225):411-415
ROSSER and SCHOENFELD have used the fact that the first 3,500,000 zeros of the RIEMANN zeta function lie on the critical line to give estimates on and . With an improvement of the above result by BRENTet al., we are able to improve these estimates and to show that the prime is greater than for . We give further results without proof.
20.
Kit C. Chan Zeljko Cuckovic 《Transactions of the American Mathematical Society》1999,351(4):1445-1460
Using the functional calculus for a normal operator, we provide a result for generalized Toeplitz operators, analogous to the theorem of Axler and Shields on harmonic extensions of the disc algebra. Besides that result, we prove that if is an injective subnormal weighted shift, then any two nontrivial subspaces invariant under cannot be orthogonal to each other. Then we show that the -algebra generated by and the identity operator contains all the compact operators as its commutator ideal, and we give a characterization of that -algebra in terms of generalized Toeplitz operators. Motivated by these results, we further obtain their several-variable analogues, which generalize and unify Coburn's theorems for the Hardy space and the Bergman space of the unit ball.