共查询到20条相似文献,搜索用时 31 毫秒
1.
Florin Radulescu 《Proceedings of the American Mathematical Society》2000,128(8):2405-2411
We prove that the algebra , a free group with finitely many generators, contains a subnormal operator such that the linear span of the set is weakly dense in . This is the analogue for the factor , finite, of a well known fact about the unilateral shift on a Hilbert space : the linear span of all the monomials is weakly dense in .
We also show that for a suitable space of square summable analytic functions, if is the projection from the Hilbert space of all square summable functions onto and is the unbounded operator of multiplication by on , then the (unbounded) operator is nonzero (with nonzero domain).
2.
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.
3.
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 .
4.
Ibrahim Assem Dieter Happel Sonia Trepode 《Proceedings of the American Mathematical Society》2000,128(8):2223-2232
We show that, if is a representation-finite iterated tilted algebra of euclidean type , then there exist a sequence of algebras , and a sequence of modules , where , such that each is an APR-tilting -module, or an APR-cotilting -module, and is tilted representation-finite.
5.
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 .
6.
Rauno Aulaskari Hasi Wulan Ruhan Zhao 《Proceedings of the American Mathematical Society》2000,128(8):2329-2335
For let be the Möbius transformation defined by , and let be the Green's function of the unit disk . We construct an analytic function belonging to for all , , but not belonging to meromorphic in and for any , . This gives a clear difference as compared to the analytic case where the corresponding function spaces ( and ) are same.
7.
Daniel Wulbert 《Proceedings of the American Mathematical Society》2000,128(8):2431-2438
Let be a -finite, nonatomic, Baire measure space. Let be a finite dimensional subspace of . There is a bounded, continuous function, , defined on , such that
(1) for all , and (2) almost everywhere.
8.
Alexander Kleshchev Alexander Premet 《Proceedings of the American Mathematical Society》2000,128(3):647-655
Let be an algebraic number field and be the ring of integers of . Let be a finite group and be a finitely generated torsion free -module. We say that is a globally irreducible -module if, for every maximal ideal of , the -module is irreducible, where stands for the residue field .
Answering a question of Pham Huu Tiep, we prove that the symmetric group does not have non-trivial globally irreducible modules. More precisely we establish that if is a globally irreducible -module, then is an -module of rank with the trivial or sign action of .
9.
Larry Smith 《Proceedings of the American Mathematical Society》2000,128(8):2199-2201
Let be a finite group and a complex representation. Barbara Schmid has shown that the algebra of invariant polynomial functions on the vector space is generated by homogeneous polynomials of degree at most , where is the largest degree of a generator in a minimal generating set for , and is the complex regular representation of . In this note we give a new proof of this result, and at the same time extend it to fields whose characteristic is larger than , the order of the group .
10.
Let be a prime number and let be the group of all invertible matrices over the prime field . It is known that every irreducible -module can occur as a submodule of , the polynomial algebra with variables over . Given an irreducible -module , the purpose of this paper is to find out the first value of the degree of which occurs as a submodule of , the subset of consisting of homogeneous polynomials of degree . This generalizes Schwartz-Tri's result to the case of any prime .
11.
Hsin-Ju Wang 《Proceedings of the American Mathematical Society》2000,128(4):963-973
Let be a -dimensional Cohen-Macaulay local ring with infinite residue field. Let be an -primary ideal of . In this paper, we prove that if for some minimal reduction of , then depth .
12.
Let be an integer and let be a domain of . Let be an injective mapping which takes hyperspheres whose interior is contained in to hyperspheres in . Then is the restriction of a Möbius transformation.
13.
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 .
14.
Djalil Kateb 《Proceedings of the American Mathematical Society》2000,128(3):735-743
Soient , et trois réels tels que , , et et soit une fonction appartenant à l'espace de Besov . Nous montrons que si est une fonction, de la variable réelle, nulle à l'origine, lipschitzienne et appartenant à l'espace on a alors . La preuve est essentiellement basée sur des résultats d'approximation par des fonctions splines de degré .
15.
Michel Van den Bergh 《Proceedings of the American Mathematical Society》2000,128(2):375-381
Assume that is a surface over an algebraically closed field . Let be obtained from by blowing up a smooth point and let be the exceptional curve. Let be the category of coherent sheaves on . In this note we show how to recover from , if we know the object .
16.
Let be a graph. We determine all graphs which are -like. We also prove that if are graphs, then in order that each -like continuum be -indecomposable for some it is necessary and sufficient that if is a graph, then is not -like for some integer with . This generalizes a well known theorem of Burgess.
17.
Guia Medolla Alberto G. Setti 《Proceedings of the American Mathematical Society》2000,128(6):1733-1742
Let be a homogeneous tree of degree , , the Laplace operator of and the fundamental solution of the heat equation on . We show that the heat kernel is asymptotically concentrated in an annulus moving to infinity with finite speed . Asymptotic concentration of heat in the norm is also investigated.
18.
Giovanni Stegel 《Proceedings of the American Mathematical Society》2000,128(6):1807-1812
Consider a discrete group and a bounded self-adjoint convolution operator on ; let be the spectrum of . The spectral theorem gives a unitary isomorphism between and a direct sum , where , and is a regular Borel measure supported on . Through this isomorphism corresponds to multiplication by the identity function on each summand. We prove that a nonzero function and its transform cannot be simultaneously concentrated on sets , such that and the cardinality of are both small. This can be regarded as an extension to this context of Heisenberg's classical uncertainty principle.
19.
Wen-ling Huang 《Proceedings of the American Mathematical Society》2000,128(8):2451-2455
In the space of invariant -dimensional subspaces of a null system in -dimensional projective space, W.L. Chow characterized the basic group of transformations as all the bijections , for which both and preserve adjacency. In the present paper we show that the two conditions is a surjection and preserves adjacency are sufficient to characterize the basic group. At the end of this paper we give an application to Lie geometry.
20.
Let . Let be an ideal of and let be the maximal ideal of such that . Then . In particular, if is square free, then is self-normalized in .