首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 109 毫秒
1.

Let be a certain Banach space consisting of continuous functions defined on the open unit disk. Let be a univalent function defined on , and assume that denotes the operator of multiplication by . We characterize the structure of the operator such that . We show that for some function in . We also characterize the commutant of under certain conditions.

  相似文献   


2.

A commutative Banach algebra is said to have the property if the following holds: Let be a closed subspace of finite codimension such that, for every , the Gelfand transform has at least distinct zeros in , the maximal ideal space of . Then there exists a subset of of cardinality such that vanishes on , the set of common zeros of . In this paper we show that if is compact and nowhere dense, then , the uniform closure of the space of rational functions with poles off , has the property for all . We also investigate the property for the algebra of real continuous functions on a compact Hausdorff space.

  相似文献   


3.
Let be a prime, and let be a finite -group acted on by an elementary abelian -group . The following results are proved:

1. If and is nilpotent of class at most for any , then the group is nilpotent of -bounded class.

2. If and is nilpotent of class at most for any , then the derived group is nilpotent of -bounded class.

  相似文献   


4.

Let be a rank two Chevalley group and be the corresponding Moufang polygon. J. Tits proved that is the universal completion of the amalgam formed by three subgroups of : the stabilizer of a point of , the stabilizer of a line incident with , and the stabilizer of an apartment passing through and . We prove a slightly stronger result, in which the exact structure of is not required. Our result can be used in conjunction with the ``weak -pair" theorem of Delgado and Stellmacher in order to identify subgroups of finite groups generated by minimal parabolics.

  相似文献   


5.

We characterize all simple unitarizable representations of the braid group on complex vector spaces of dimension . In particular, we prove that if and denote the two generating twists of , then a simple representation (for ) is unitarizable if and only if the eigenvalues of are distinct, satisfy and 0$"> for , where the are functions of the eigenvalues, explicitly described in this paper.

  相似文献   


6.

Let be a monic polynomial of degree , with complex coefficients, and let be its monic factor. We prove an asymptotically sharp inequality of the form , where denotes the sup norm on a compact set in the plane. The best constant in this inequality is found by potential theoretic methods. We also consider applications of the general result to the cases of a disk and a segment.

  相似文献   


7.

Suppose is a complex Hilbert space and is a bounded operator. For each closed set let denote the corresponding spectral manifold. Let denote the set of all points with the property that for any open neighborhood of In this paper we show that if is dominating in some bounded open set, then has a nontrivial invariant subspace. As a corollary, every Hilbert space operator which is a quasiaffine transform of a subdecomposable operator with large spectrum has a nontrivial invariant subspace.

  相似文献   


8.

A Lie subalgebra of is said to be finitary if it consists of elements of finite rank. We show that, if acts irreducibly on , and if is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of acts irreducibly on too. When , it follows that the locally solvable radical of such is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic are hyperabelian.

  相似文献   


9.

Let be a deformation of a normal Gorenstein surface singularity over the complex number field . We assume that is a neighborhood of the origin of . Then we prove that admits a simultaneous log-canonical model if and only if an invariant of each fiber is constant.

  相似文献   


10.

This article presents sufficient conditions for the positive definiteness of radial functions , , in terms of the derivatives of . The criterion extends and unifies the previous analogues of Pólya's theorem and applies to arbitrarily smooth functions. In particular, it provides upper bounds on the Kuttner-Golubov function which gives the minimal value of such that the truncated power function , , is positive definite. Analogous problems and criteria of Pólya type for -dependent functions, 0$">, are also considered.

  相似文献   


设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号