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1.
Let be a finite -solvable group for different primes and . Let and be such that . We prove that every of -degree has -degree if and only if and .
2.
Jutta Hausen Phillip Schultz 《Proceedings of the American Mathematical Society》1998,126(9):2525-2533
Let be a prime number and let be an abelian -group. Let be the maximal normal -subgroup of and the maximal -subgroup of its centre. Let be the torsion radical of . Then . The result is new for and 3, and the proof is new and valid for all primes .
3.
E. Ballico 《Proceedings of the American Mathematical Society》1999,127(9):2527-2528
Fix integers with and ; if assume . Let be general points of the complex projective space and let be the blow up of at with exceptional divisors , . Set . Here we prove that the divisor is ample if and only if , i.e. if and only if .
4.
Sultan Catto Jonathan Huntley Jay Jorgenson David Tepper 《Proceedings of the American Mathematical Society》1998,126(12):3455-3459
Let be the homogeneous space associated to the group
. Let where and consider the first nontrivial eigenvalue of the Laplacian on . Using geometric considerations, we prove the inequality . Since the continuous spectrum is represented by the band , our bound on can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.
. Let where and consider the first nontrivial eigenvalue of the Laplacian on . Using geometric considerations, we prove the inequality . Since the continuous spectrum is represented by the band , our bound on can be viewed as an analogue of Selberg's eigenvalue conjecture for quotients of the hyperbolic half space.
5.
Sergei Yu. Vasilovsky 《Proceedings of the American Mathematical Society》1999,127(12):3517-3524
The algebra of all matrices over a field has a natural -grading . In this paper graded identities of the -graded algebra over a field of characteristic zero are studied. It is shown that all the -graded polynomial identities of follow from the following:
6.
Abdelmalek Azizi 《Proceedings of the American Mathematical Society》2002,130(8):2197-2202
Let and be prime numbers such that and . Let , , and let be the 2-Hilbert class field of , the 2-Hilbert class field of and the Galois group of . The 2-part of the class group of is of type , so contains three extensions . Our goal is to study the problem of capitulation of the 2-classes of in , and to determine the structure of .
RS
7.
Muneo Cho 《Proceedings of the American Mathematical Society》2000,128(8):2357-2363
Let be a doubly commuting -tuple of -hyponormal operators with unitary operators from the polar decompositions . Let and . In this paper, we will show relations between the Taylor spectrum and the Xia spectrum .
8.
Karel Dekimpe 《Proceedings of the American Mathematical Society》2003,131(3):973-978
We are dealing with Lie groups which are diffeomorphic to , for some . After identifying with , the multiplication on can be seen as a map . We show that if is a polynomial map in one of the two (sets of) variables or , then is solvable. Moreover, if one knows that is polynomial in one of the variables, the group is nilpotent if and only if is polynomial in both its variables.
9.
Shinji Adachi Kazunaga Tanaka 《Proceedings of the American Mathematical Society》2000,128(7):2051-2057
We study Trudinger type inequalities in and their best exponents . We show for , ( is the surface area of the unit sphere in ), there exists a constant such that
for all . Here is defined by
It is also shown that with is false, which is different from the usual Trudinger's inequalities in bounded domains.
10.
Elijah Liflyand Ferenc Mó ricz 《Proceedings of the American Mathematical Society》2000,128(5):1391-1396
We prove that the Hausdorff operator generated by a function is bounded on the real Hardy space . The proof is based on the closed graph theorem and on the fact that if a function in is such that its Fourier transform equals for (or for ), then .
11.
Assume and is a Lipschitz -mapping; and denote the volume and the surface area of . We verify that there exists a figure with , and, of course, , where depends only on the dimension and on . We also give an example when is a square and ; in fact, the boundary of can contain a fractal of Hausdorff dimension exceeding one.
12.
Tianxuan Miao 《Proceedings of the American Mathematical Society》1998,126(12):3571-3579
Let be a -compact locally compact nondiscrete group and let be a -invariant ideal of . We denote the set of left invariant means on that are zero on (i.e. for all ) by . We show that, when is amenable as a discrete group and the closed -invariant subset of the spectrum of corresponding to is a -set, is very large in the sense that every nonempty -subset of contains a norm discrete copy of , where is the Stone- compactification of the set of positive integers with the discrete topology. In particular, we prove that has no exposed points in this case and every nonempty -subset of the set of left invariant means on contains a norm discrete copy of .
13.
Akira Yamada 《Proceedings of the American Mathematical Society》1999,127(5):1399-1408
Let be a planar regular region whose Schottky double has genus and set . For fixed we determine the range of the function where is the Riemann theta function on . Also we introduce two weighted Hardy spaces to study the problem when the matrix is positive definite. The proof relies on new theta identities using Fay's trisecants formula.
14.
Diane Benjamin 《Proceedings of the American Mathematical Society》1999,127(2):371-376
Let denote the largest irreducible character degree of a finite group , and let be a prime. Two results are obtained. First, we show that, if is a -solvable group and if , then . Next, we restrict attention to solvable groups and show that, if and if is a Sylow -subgroup of , then .
15.
Florin Pop 《Proceedings of the American Mathematical Society》1998,126(10):2987-2992
If is an inclusion of type factors with we study the connection between the existence of singular states on which extend the trace on and the Dixmier approximation property in with unitaries in We also prove the existence of singular conditional expectations from certain free product factors onto irreducible hyperfinite subfactors.
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.
Hermann Render 《Proceedings of the American Mathematical Society》1999,127(5):1409-1411
It is shown that the space of all regular maximal ideals in the Banach algebra with respect to the Hadamard product is isomorphic to The multiplicative functionals are exactly the evaluations at the -th Taylor coefficient. It is a consequence that for a given function in and for a function holomorphic in a neighborhood of with and for all the function is in
18.
Ferenc Weisz 《Proceedings of the American Mathematical Society》2000,128(8):2337-2345
The -dimensional dyadic martingale Hardy spaces are introduced and it is proved that the maximal operator of the means of a Walsh-Fourier series is bounded from to and is of weak type , provided that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain that the means of a function converge a.e. to the function in question. Moreover, we prove that the means are uniformly bounded on whenever . Thus, in case , the means converge to in norm. The same results are proved for the conjugate means, too.
19.
Torben Maack Bisgaard 《Proceedings of the American Mathematical Society》1998,126(11):3227-3237
For a certain constant (a little less than ), every function satisfying , , is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence there is a positive definite matrix sequence which is not of positive type and which satisfies , . For a certain constant (a little greater than ), for every function satisfying , , there is a convolution semigroup of measures on , with moments of all orders, such that , , and for every such convolution semigroup the measure is Stieltjes indeterminate for all .
20.
Let denote the Schlumprecht space. We prove that
(1) is finitely disjointly representable in ;
(2) contains an -spreading model;
(3) for any sequence of natural numbers, is isomorphic to the space .