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Hahn-Banach for Riesz homomorphisms Riesz同态的Hahn-Banach
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80014-9
G.J.H.M. Buskes , A.C.M. van Rooij
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引用次数: 15
On some q-operators with applications 关于一些q-算子的应用
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80011-3
N.A. Al-Salam
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引用次数: 6
Representations of the twisted SU(2) quantum group and some q-hypergeometric orthogonal polynomials 扭曲SU(2)量子群的表示和一些q-超几何正交多项式
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80020-4
T.H. Koornwinder

The matrix elements of the irreducible unitary representations of the twisted SU(2) quantum group are computed explicitly. It is shown that they can be identified with two different classes of p-hypergeometric orthogonal polynomials: with the little q-Jacobi polynomials and with certain q-analogues of Krawtchouk polynomials. The orthogonality relations for these polynomials correspond to Schur type orthogonality relations in the first case and to the unitarity conditions for the representations in the second case. The paper also contains a new proof of Woronowicz' classification of the unitary irreducible representations of this quantum group. It avoids infinitesimal methods. Symmetries of the matrix elements of the irreducible unitary representations are proved without using the explicit expressions.

明确地计算了扭曲SU(2)量子群的不可约酉表示的矩阵元素。证明了它们可以用两类不同的p-超几何正交多项式来识别:小q-Jacobi多项式和某些q-类似的Krawtchouk多项式。这些多项式的正交关系对应于第一种情况下的舒尔型正交关系和第二种情况下表示的统一条件。本文还对该量子群的幺正不可约表示的Woronowicz分类给出了新的证明。它避免了无穷小的方法。在不使用显式表达式的情况下,证明了不可约酉表示的矩阵元素的对称性。
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引用次数: 109
On the non-rationality of the Fano variety of ℙ5, which contains three planes two by two meeting in one point 关于包含在一点上的三个2乘2的平面的法诺变换的不合理性
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80012-5
Elisabetta Ambrogio , Daniela Romagnoli

We prove that the Fano variety W of degree 6 in ℙ5, complete intersection of a smooth quadric hypersurface with a smooth cubic hypersurface of ℙ5, is not rational if it contains 3 planes two by two meeting at least in one point.

证明了一个光滑的二次超曲面与一个光滑的三次超曲面的完全交,如果它包含3个2乘2的平面至少在一个点上相交,那么在一个光滑的二次超曲面中6次的Fano变化W是不合理的。
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引用次数: 0
A characterization of Riesz spaces which are Riesz isomorphic to C(X) for some completely regular space X 对于某完全正则空间X,与C(X) Riesz同构的Riesz空间的刻划
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80019-8
Hong-Yun Xiong

Let E be an Archimedean Riesz space possessing a weak unit e and let Ω be the collection of all Riesz homomorphisms ø from E onto ℝ such that ø(e)=1. The Gelfand mapping G :xx^ on E is defined by x^(ø) = ø(x) for all ø∈Ω. We endow Ω with the topology induced by E (i.e., the weakest topology such that each x^ is continuous on Ω). The principal ideal in E generated by e is denoted by Id(e). The main theorem in this paper says that the following statements (A) and (B) are equivalent.

  • (A)

    There exists a completely regular space X such that E is Riesz isomorphic to the space C(X) of all real continuous functions on X.

  • (B)

    The following conditions for the Riesz space E hold: (1) E is Archimedean and has a weak unit e; (2) Ω separates the points of E; (3) E is uniformly complete; (4) G(Id(e)) is norm dense in the space Cb(Ω) of all real bounded continuous functions on Ω; (5) E is 2-universally complete with carrier space Ω.

Some other conditions are mentioned and an example is given to show that condition (5) is necessary for (B) ⇒(A).

设E是一个具有弱单位E的阿基米德Riesz空间,设Ω是从E到l的所有Riesz同态的集合,且ø(E)=1。对于所有ø∈Ω, Gelfand映射G:x→x^ on E定义为x^(ø) = ø(x)。我们赋予Ω由E引起的拓扑(即,使每个x^在Ω上连续的最弱拓扑)。由E生成的E中的主理想用Id(E)表示。本文的主要定理表明下列表述(A)与(B)是等价的:(A)存在一个完全正则空间X,使得E与X上所有实连续函数的空间C(X)是Riesz同构的(B) Riesz空间E成立下列条件:(1)E是阿基米德的,且有一个弱单位E;(2) Ω将E点分开;(3) E均匀完备;(4)在Ω上所有实数有界连续函数的Cb(Ω)空间中G(Id(e))是范数密集的;(5) E是2-普遍完备的载流子空间Ω。文中还提到了其他一些条件,并给出了一个例子来说明条件(5)对于(B)⇒(A)是必要的。
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引用次数: 9
Polynomial congruences over incomplete residue systems, modulo k 不完全剩余系统上的多项式同余,模k
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80016-2
J.H.H. Chalk

This is a sequel to the previous article (Proceedings Kon. Ned. Akad. van Wetensch., A 83 (4), (1980), 367–374, see MR, 82d: 10053, 10G10.) on the Mordell and Tietäväinen inequalities for the distribution of zeros of polynomial congruences in incomplete residue systems modulo k. Here the emphasis is on composite k and applies to a general class of polynomials satisfying mild conditions of non-degeneracy for each prime pk.

这是上一篇文章的续集。内德。Akad。范Wetensch。(A 83(4),(1980), 367-374,见MR, 82d: 10053, 10G10.)关于模k的不完全剩余系统中多项式同余的零分布的Mordell不等式和Tietäväinen不等式。这里的重点是复合k,并适用于满足每个素数p∣k的非退化的温和条件的一般多项式类。
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引用次数: 12
Derative of analytic elements on infraconnected clopen sets 次连通开集上解析元的导数
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80017-4
Alain Escassut
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引用次数: 3
Some theorems on semi-prime non-associative rings 半素非结合环上的几个定理
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80013-7
A.H. Boers
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引用次数: 2
On Veronesean surfaces 在Veronesean表面上
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80018-6
Alessandro Gimigliano
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引用次数: 37
A characterization of dual Banach lattices 对偶Banach格的表征
Pub Date : 1989-03-20 DOI: 10.1016/S1385-7258(89)80015-0
V. Caselles

In this paper we give a characterization of dual Banach lattices. In fact, we prove that a Banach function space E on a separable measure space which has the Fatou property is a dual Banach lattice if and only if all positive operators from L1(0,1) into E are abstract kernel operators, hence extending the fact, proved by M. Talagrand, that separable Banach lattices with the Radon-Nikodym property are dual Banach lattices.

本文给出了对偶巴拿赫格的一个表征。事实上,我们证明了具有Fatou性质的可分离测度空间上的Banach函数空间E是对偶Banach格当且仅当从L1(0,1)到E的所有正算子都是抽象核算子,从而推广了M. Talagrand证明的具有Radon-Nikodym性质的可分离Banach格是对偶Banach格的事实。
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引用次数: 1
期刊
Indagationes Mathematicae (Proceedings)
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