共查询到20条相似文献,搜索用时 31 毫秒
1.
P. M. Gadea J. Muñ oz Masqué 《Proceedings of the American Mathematical Society》1996,124(5):1437-1443
Let be a finite-dimensional commutative algebra over and let , and be the ring of -differentiable functions of class , the ring of real analytic mappings with values in and the ring of -analytic functions, respectively, defined on an open subset of . We prove two basic results concerning -differentiability and -analyticity: ) , ) if and only if is defined over .
2.
Jon F. Carlson Hans-Werner Henn 《Proceedings of the American Mathematical Society》1996,124(3):665-670
Suppose that is a compact Lie group or a discrete group of finite virtual cohomological dimension and that is a field of characteristic . Suppose that is a set of elementary abelian -subgroups such that the cohomology is detected on the centralizers of the elements of . Assume also that is closed under conjugation and that is in whenever some subgroup of is in . Then there exists a regular element in the cohomology ring such that the restriction of to an elementary abelian -subgroup is not nilpotent if and only if is in . The converse of the result is a theorem of Lannes, Schwartz and the second author. The results have several implications for the depth and associated primes of the cohomology rings.
3.
Meng-Kiat Chuah 《Proceedings of the American Mathematical Society》1996,124(11):3481-3491
Let be a compact semi-simple Lie group, and let be a maximal unipotent subgroup of the complexified group . In this paper, we classify all the -invariant Kaehler structures on . For each Kaehler structure , let be the line bundle with connection whose curvature is . We then study the holomorphic sections of , which constitute a -representation space.
4.
Sophie Frisch 《Proceedings of the American Mathematical Society》1996,124(12):3595-3604
If is a subring of a Krull ring such that is a valuation ring for every finite index , in Spec, we construct polynomials that map into the maximal possible (for a monic polynomial of fixed degree) power of , for all in Spec simultaneously. This gives a direct sum decomposition of Int, the -module of polynomials with coefficients in the quotient field of that map into , and a criterion when Int has a regular basis (one consisting of 1 polynomial of each non-negative degree).
5.
Simba A. Mutangadura 《Proceedings of the American Mathematical Society》1996,124(3):907-918
We continue here the study begun in earlier papers on implementation of comparative probability by states. Let be a von Neumann algebra on a Hilbert space and let denote the projections of . A comparative probability (CP) on (or more correctly on is a preorder on satisfying:
- with for some .
- If , then either or .
- If , and are all in and , , then .
6.
For a separable infinite-dimensional Hilbert space , we consider the full algebra of bounded linear transformations and the unique non-trivial norm-closed two-sided ideal of compact operators . We also consider the quotient -algebra with quotient map
For any -subalgebra of , the relative commutant is given by for all in . It was shown by D. Voiculescu that, for any separable unital -subalgebra of ,
In this note, we exhibit a non-separable unital -subalgebra of for which (VDCT) fails.
7.
Haruto Ohta 《Proceedings of the American Mathematical Society》1996,124(3):961-967
Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups.
8.
Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that
where as and .
9.
F. Ghahramani R. J. Loy G. A. Willis 《Proceedings of the American Mathematical Society》1996,124(5):1489-1497
For a Banach algebra , amenability of necessitates amenability of , and similarly for weak amenability provided is a left ideal in . For a locally compact group, indeed more generally, is amenable if and only if is finite. If is weakly amenable, then is weakly amenable.
10.
Let be a real Banach space with norm and let be a nonexpansive sequence in (i.e., for all ). Let . We deal with the mean point of concerning a Banach limit. We show that if is reflexive and , then and there exists a unique point with such that . This result is applied to obtain the weak and strong convergence of .
11.
Let be a finite collection of commuting self-adjoint elements of a von Neumann algebra . Then within the (abelian) C*-algebra they generate, these elements have a least upper bound . We show that within , is a minimal upper bound in the sense that if is any self-adjoint element such that for all , then . The corresponding assertion for infinite collections is shown to be false in general, although it does hold in any finite von Neumann algebra. We use this sort of result to show that if are von Neumann algebras, is a faithful conditional expectation, and is positive, then converges in the strong operator topology to the ``spectral order majorant' of in .
12.
Bosko Zivaljevic 《Proceedings of the American Mathematical Society》1996,124(7):2205-2210
For every and non-Borel subset of an internal set in a saturated nonstandard universe there exists an internal, unbounded, non-atomic measure so that is not finite for any Borel set in
13.
On a polynomial inequality of Kolmogoroff's type 总被引:1,自引:0,他引:1
We prove an inequality of the form
for polynomials of degree and any fixed . Here is the -norm on with a weight . The coefficients and are given explicitly and depend on and only. The equality is attained for the Hermite orthogonal polynomials .
14.
B. Kaminski 《Proceedings of the American Mathematical Society》1996,124(5):1533-1537
It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.
15.
Jianhong Shen Gilbert Strang 《Proceedings of the American Mathematical Society》1996,124(12):3819-3833
To study wavelets and filter banks of high order, we begin with the zeros of . This is the binomial series for , truncated after terms. Its zeros give the zeros of the Daubechies filter inside the unit circle, by . The filter has additional zeros at , and this construction makes it orthogonal and maximally flat. The dilation equation leads to orthogonal wavelets with vanishing moments. Symmetric biorthogonal wavelets (generally better in image compression) come similarly from a subset of the zeros of . We study the asymptotic behavior of these zeros. Matlab shows a remarkable plot for . The zeros approach a limiting curve in the complex plane, which is the circle . All zeros have , and the rightmost zeros approach (corresponding to ) with speed . The curve gives a very accurate approximation for finite . The wide dynamic range in the coefficients of makes the zeros difficult to compute for large . Rescaling by allows us to reach by standard codes.
16.
Yibiao Pan 《Proceedings of the American Mathematical Society》1996,124(9):2821-2825
We consider boundedness properties of oscillatory singular integrals on and Hardy spaces. By constructing a phase function, we prove that boundedness may fail while boundedness holds for all . This shows that the theory and theory for such operators are fundamentally different.
17.
A. Cuyt K. Driver D. S. Lubinsky 《Proceedings of the American Mathematical Society》1996,124(7):2123-2136
In the convergence theory of rational interpolation and Padé approximation, it is essential to estimate the size of the lemniscatic set and , for a polynomial of degree . Usually, is taken to be monic, and either Cartan's Lemma or potential theory is used to estimate the size of , in terms of Hausdorff contents, planar Lebesgue measure , or logarithmic capacity cap. Here we normalize and show that cap and are the sharp estimates for the size of . Our main result, however, involves generalizations of this to polynomials in several variables, as measured by Lebesgue measure on or product capacity and Favarov's capacity. Several of our estimates are sharp with respect to order in and .
18.
S. W. Seif 《Proceedings of the American Mathematical Society》1996,124(5):1361-1370
For an arbitrary algebra a new labelling, called the signed labelling, of the Hasse diagram of is described. Under the signed labelling, each edge of the Hasse diagram of receives a label from the set . The signed labelling depends completely on a subset of the unary polynomials of and its inspiration comes from semigroup theory. For finite algebras, the signed labelling complements the labelled congruence lattices of tame congruence theory (TCT). It provides a different kind of information about those algebras than the TCT labelling particularly with regard to congruence semimodularity. The main result of this paper shows that the congruence lattice of any algebra admits a natural join congruence, denoted , such that satisfies the semimodular law. In an application of that result, it is shown that for a regular semigroup , for which in , is actually a lattice congruence, coincides with , and satisfies the semimodular law.
19.
Oleg V. Belegradek 《Proceedings of the American Mathematical Society》1996,124(2):623-625
We show that for any arithmetical -degree there is a first order decision problem such that has -degree for the free 2-step nilpotent group of rank 2. This implies a conjecture of Sacerdote.
20.
Yuji Yoshino 《Proceedings of the American Mathematical Society》1996,124(9):2641-2647
Let be a Gorenstein complete local ring. Auslander's higher delta invariants are denoted by for each module and for each integer . We propose a conjecture asking if for any positive integers and . We prove that this is true provided the associated graded ring of has depth not less than . Furthermore we show that there are only finitely many possibilities for a pair of positive integers for which .