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1.
Jin-Hong Kim 《Proceedings of the American Mathematical Society》2000,128(3):865-871
In this article we show that when the structure group of the reducible principal bundle is and is an -subbundle of , the rank of the holonomy group of a connection which is gauge equivalent to its conjugate connection is less than or equal to , and use the estimate to show that for all odd prime , if the holonomy group of the irreducible connection as above is simple and is not isomorphic to , , or , then it is isomorphic to .
2.
Ignacio Villanueva 《Proceedings of the American Mathematical Society》2000,128(3):793-801
Given a -linear operator from a product of spaces into a Banach space , our main result proves the equivalence between being completely continuous, having an -valued separately continuous extension to the product of the biduals and having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to being weakly compact, and that, for , being weakly compact implies the conditions above but the converse fails.
3.
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 .
4.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2000,128(2):353-360
Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .
5.
Harald K. Wimmer 《Proceedings of the American Mathematical Society》2000,128(3):873-876
Let and be complementary spaces of a finite dimensional unitary space and let denote the projection of on parallel to . Estimates for the norm of are derived which involve the norm of the restriction of to or the gap between and .
6.
Hisao Taya 《Proceedings of the American Mathematical Society》2000,128(5):1285-1292
Let be a square-free integer with and . Put and . For the cyclotomic -extension of , we denote by the -th layer of over . We prove that the -Sylow subgroup of the ideal class group of is trivial for all integers if and only if the class number of is not divisible by the prime . This enables us to show that there exist infinitely many real quadratic fields in which splits and whose Iwasawa -invariant vanishes.
7.
A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map from into , where is a hypersurface in a complex Banach manifold and is a hyperbolic Banach space. Under various assumptions on , and we show that can be extended to a holomorphic map from into . Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property.
8.
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.
9.
Robert Myers 《Proceedings of the American Mathematical Society》2000,128(5):1563-1566
This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open -manifold which is not homeomorphic to is a covering space of an -manifold and either or and is irreducible, then the group of covering translations injects into the homeotopy group of .
10.
Paolo Lipparini 《Proceedings of the American Mathematical Society》2000,128(2):605-609
We prove the following: Theorem A. If is a -regular ultrafilter, then either
- (a)
- is -regular, or
- (b)
- the cofinality of the linear order is , and is -regular for all .
11.
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.
12.
We prove that for every -hyponormal operator there corresponds a hyponormal operator such that and have ``equal spectral structure". We also prove that every -hyponormal operator is subdecomposable. Then some relevant quasisimilarity results are obtained, including that two quasisimilar -hyponormal operators have equal essential spectra.
13.
Wojciech Szymanski 《Proceedings of the American Mathematical Society》2000,128(3):789-791
We show that if are type factors with finite index (and common identity) and is the trace preserving conditional expectation, then there are no subdiagonal algebras in with respect to unless .
14.
Dmitry N. Kozlov 《Proceedings of the American Mathematical Society》2000,128(8):2253-2259
Let denote the order complex of the partition lattice. The natural -action on the set induces an -action on . We show that the regular CW complex is collapsible. Even more, we show that is collapsible, where is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual way several previous results regarding the multiplicity of the trivial character in the -representation on .
15.
It is shown that the Bochner-Riesz operator on of negative order is of restricted weak type in the critical points and , where , for in the two-dimensional case and , for if .
16.
Mikhail G. Tkacenko Vladimir V. Tkachuk Richard G. Wilson Ivan V. Yaschenko 《Proceedings of the American Mathematical Society》2000,128(1):287-297
Two -topologies and given on the same set , are called transversal if their union generates the discrete topology on . The topologies and are -complementary if they are transversal and their intersection is the cofinite topology on . We establish that for any connected Tychonoff topology there exists a connected Tychonoff transversal one. Another result is that no -complementary topology exists for the maximal topology constructed by van Douwen on the rational numbers. This gives a negative answer to Problem 162 from Open Problems in Topology (1990).
17.
M. Beattie S. Dascalescu L. Grü nenfelder 《Proceedings of the American Mathematical Society》2000,128(2):361-367
In this note we describe nonsemisimple Hopf algebras of dimension with coradical isomorphic to , abelian of order , over an algebraically closed field of characteristic zero. If is cyclic or , then we also determine the number of isomorphism classes of such Hopf algebras.
18.
David R. Richman proved that for every integral matrix is a sum of seven -th powers. In this paper, in light of a question proposed earlier by M. Newman for the ring of integers of an algebraic number field, we obtain a discriminant criterion for every matrix over an order of an algebraic number field to be a sum of (seven) -th powers.
19.
We consider the problem of the classification of semisimple Hopf algebras of dimension where are two prime numbers. First we prove that the order of the group of grouplike elements of is not , and that if it is , then . We use it to prove that if and its dual Hopf algebra are of Frobenius type, then is either a group algebra or a dual of a group algebra. Finally, we give a complete classification in dimension , and a partial classification in dimensions and .
20.
Simeon T. Stefanov 《Proceedings of the American Mathematical Society》2000,128(3):885-891
For any a -dimensional polyhedron is constructed such that the Yang index of its deleted product equals . This answers a question of Izydorek and Jaworowski (1995). For any a -dimensional closed manifold with involution is constructed such that , but can be mapped into a -dimensional polyhedron without antipodal coincidence.