共查询到20条相似文献,搜索用时 31 毫秒
1.
Wang Jian 《数学年刊B辑(英文版)》1988,9(4):494-499
Lei D be a domain in the complex plane, and H~∞(D) be the Banach algebra ofbounded analytic functions on D. Rosenblum proved a corona theorem for countably manyfunctions on the open unit disk, Rudol extended the result to the finitely connected domains.In this paper the author uses Behrens' idea to extend the result to a class of infinitelyconnected domains. 相似文献
2.
Jie Xiao 《manuscripta mathematica》1998,97(2):217-232
For , let and be the spaces of multipliers of , the Sobolev space on the unit circle, and , the Dirichlet type space on the open unit disk, respectively. In fact,
and are obtained from and by analytic extension. In this paper, we show that if is an -Carleson measure on the open unit disk, then there exists a function f defined on the closed unit disk such that the equation holds on the open unit disk, and such that the boundary value function f belongs to
. For applications, we first establish the corona theorem for , which, in the case , gives the answer to a question of L. Brown and A. L. Shields. Secondly, we obtain a geometric characterization of the interpolating
sequences for with that extends a theorem of D. E. Marshall and C. Sundberg.
Received: 20 October 1997 / Revised version: 7 May 1998 相似文献
3.
Yaakov Ben Natan Yoav Benyamini H»kan Hendenmalm Yitzhak Weit 《Arkiv f?r Matematik》1996,34(2):199-224
Our main result gives necessary and sufficient conditions, in terms of Fourier transforms, for an ideal in the convolution
algebra of spherical integrable functions on the (conformal) automorphism group of the unit disk to be dense, or to have as
closure the closed ideal of functions with integral zero. This is then used to prove a generalization of Furstenberg's theorem,
which characterizes harmonic functions on the unit disk by a mean value property, and a “two circles” Morera type theorem
(earlier announced by Agranovskii).
The second author's work was partially supported by the fund for the promotion of research at the Technion-Israel Institute
of Technology. The third author's work was partially supported by the Swedish Natural Science Research Council, and by the
1992 Wallenberg Prize from the Swedish Mathematical Society. 相似文献
4.
We consider here the algebra of functions which are analytic and bounded in the right half-plane and can moreover be expanded
as an ordinary Dirichlet series. We first give a new proof of a theorem of Bohr saying that this expansion converges uniformly
in each smaller half-plane; then, as a consequence of the alternative definition of this algebra as an algebra of functions
analytic in the infinite-dimensional polydisk, we first observe that it does not verify the corona theorem of Carleson; and
then, we give in a deterministic way a new quantitative proof of the Bohnenblust-Hille optimality theorem, through the construction
of a generalized Rudin-Shapiro sequence of polynomials. Finally, we compare this proof with probabilistic ones. 相似文献
5.
本文给出对数K-Carleson测度的一个新特征,并以此为工具研究QK空间的乘子代数M(QK),给出乘子代数M(QK)的某些特征描述.利用对数K-Carleson测度及QK空间的一个新特征,建立乘子代数M(QK)上的Corona定理和Wolff定理. 相似文献
6.
We prove a corona theorem for infinitely many functions from the
multiplier algebra on Dirichlet space. 相似文献
7.
《Optimization》2012,61(12):1511-1517
We present an elementary proof of the Lagrange multiplier theorem for optimization problems with equality constraints in normed linear spaces. Most proofs in the literature rely on advanced concepts and results, such as the implicit function theorem and the Lyusternik theorem. By contrast, the proof given in this article employs only basic results from linear algebra, the critical-point condition for unconstrained minima and the fact that a continuous function attains its minimum over a closed ball in the finite-dimensional space. 相似文献
8.
We present a short elementary proof of the Lagrange multiplier theorem for equality-constrained optimization. Most proofs in the literature rely on advanced analysis concepts such as the implicit function theorem, whereas elementary proofs tend to be long and involved. By contrast, our proof uses only basic facts from linear algebra, the definition of differentiability, the critical-point condition for unconstrained minima, and the fact that a continuous function attains its minimum over a closed ball. 相似文献
9.
If
\mathfrakA{\mathfrak{A}} is a unital weak-* closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property
\mathbbA1(1){\mathbb{A}_1(1)}, then the cyclic invariant subspaces index a Nevanlinna–Pick family of kernels. This yields an NP interpolation theorem for
a wide class of algebras. In particular, it applies to many function spaces over the unit disk including Bergman space. We
also show that the multiplier algebra of a complete NP space has
\mathbbA1(1){\mathbb{A}_1(1)}, and thus this result applies to all of its subalgebras. A matrix version of this result is also established. It applies,
in particular, to all unital weak-* closed subalgebras of H
∞ acting on Hardy space or on Bergman space. 相似文献
10.
Nik Weaver 《Proceedings of the American Mathematical Society》1997,125(9):2643-2648
We prove a Tietze type theorem which provides extensions of little Lipschitz functions defined on closed subsets. As a consequence, we get that the quotient of any little Lipschitz algebra by any norm-closed ideal is another little Lipschitz algebra.
11.
In this paper, we study the problem of when the corona algebra of a non-unital C*-algebra is purely infinite. A complete answer
is obtained for stabilisations of simple and unital algebras that have enough comparison of positive elements. Our result
relates the pure infiniteness condition (from its strongest to weakest forms) to the geometry of the tracial simplex of the
algebra, and to the behaviour of corona projections, despite the fact that there is no real rank zero condition. 相似文献
12.
The free nonassociative algebra has two subspaces which are closed under both the commutator and the associator: the Akivis elements and the primitive elements. Every Akivis element is primitive, but there are primitive elements which are not Akivis. Using a theorem of Shestakov, we give a recursive formula for the dimension of the Akivis elements. Using a theorem of Shestakov and Umirbaev, we prove a closed formula for the dimension of the primitive elements. These results generalize the Witt dimension formula for the Lie elements in the free associative algebra. 相似文献
13.
Yong Zhang 《Journal of Functional Analysis》2002,191(1):123-131
We show that every closed ideal of a Segal algebra on a compact group admits a central approximate identity which has the property, called condition (U), that the induced multiplication operators converge to the identity operator uniformly on compact sets of the ideal. This result extends a known one due to H. Reiter who has considered the problem under the condition that the Segal algebra is symmetric. We prove further that a closed right ideal of a Segal algebra on a compact group admits a left approximate identity satisfying condition (U) if and only if it is approximately complemented as a subspace of the Segal algebra; if in addition the Segal algebra is symmetric, then a closed left ideal admits a right approximate identity satisfying condition (U) if and only if it is approximately complemented. 相似文献
14.
Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H ∞(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H ∞(Ω) is equal to 2. The proof is based on Suárez’s theorem that the topological stable rank of H ∞( $ \mathbb{D} $ ) is equal to 2, where $ \mathbb{D} $ is the unit disk. We also show that for circular domains symmetric to the real axis, the Bass and topological stable ranks of the real-symmetric algebra H ? ∞ (Ω) are 2. 相似文献
15.
Richard M. Aron Daniel Carando T. W. Gamelin Silvia Lassalle Manuel Maestre 《Mathematische Annalen》2012,353(2):293-303
We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for ? 2 and for c 0. In the case of the open unit ball of c 0, we solve the corona problem whenever all but one of the functions comprising the corona data are uniformly approximable by polynomials in functions in ${c_0^*}$ . 相似文献
16.
Takuya Hosokawa 《Journal of Mathematical Analysis and Applications》2008,347(1):72-80
We study the extreme points of the closed convex hull of the set of all composition operators on the space of bounded analytic functions and the disk algebra. 相似文献
17.
Cristina Draper Antonio Fernández López Esther García Miguel Gómez Lozano 《Journal of Algebra》2008,319(6):2372-2394
We define the socle of a nondegenerate Lie algebra as the sum of all its minimal inner ideals. The socle turns out to be an ideal which is a direct sum of simple ideals, and satisfies the descending chain condition on principal inner ideals. Every classical finite dimensional Lie algebra coincides with its socle, while relevant examples of infinite dimensional Lie algebras with nonzero socle are the simple finitary Lie algebras and the classical Banach Lie algebras of compact operators on an infinite dimensional Hilbert space. This notion of socle for Lie algebras is compatible with the previous ones for associative algebras and Jordan systems. We conclude with a structure theorem for simple nondegenerate Lie algebras containing abelian minimal inner ideals, and as a consequence we obtain that a simple Lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank-one element. 相似文献
18.
The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of a complex (an algebra) are introduced. Cohomological range leads to the concepts of derived bounded algebra and strongly derived unbounded algebra naturally. The first and second Brauer-Thrall type theorems for the bounded derived category of a finite-dimensional algebra over an algebraically closed field are obtained. The first Brauer-Thrall type theorem says that derived bounded algebras are just derived finite algebras. The second Brauer-Thrall type theorem says that an algebra is either derived discrete or strongly derived unbounded, but not both. Moreover, piecewise hereditary algebras and derived discrete algebras are characterized as the algebras of finite global cohomological width and the algebras of finite global cohomological length respectively. 相似文献
19.
Let K be an algebraically closed field of characteristic zero and consider a set of 2×2 or 3×3 matrices. Using a theorem of Shemesh, we give conditions for when the matrices in the set generate the full matrix algebra. 相似文献
20.
Jean-Pierre Magnot 《Bulletin des Sciences Mathématiques》2004,128(6):513-529
We give a theorem of reduction of the structure group of a principal bundle P with regular structure group G. Then, when G is in the classes of regular Lie groups defined by T. Robart in [Can. J. Math. 49 (4) (1997) 820-839], we define the closed holonomy group of a connection as the minimal closed Lie subgroup of G for which the previous theorem of reduction can be applied. We also prove an infinite dimensional version of the Ambrose-Singer theorem: the Lie algebra of the holonomy group is spanned by the curvature elements. 相似文献