共查询到20条相似文献,搜索用时 15 毫秒
1.
George Androulakis Alexey I. Popov Adi Tcaciuc Vladimir G. Troitsky 《Integral Equations and Operator Theory》2009,65(4):473-484
We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on an infinite-dimensional Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators
on ℓp (1 ≤ p < ∞) or c0. 相似文献
2.
Matthew Kennedy Victor S. Shulman Yuri V. Turovskii 《Integral Equations and Operator Theory》2009,63(1):47-93
We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence
are imposed on certain components of the subgrading. This allows us to obtain some useful information about the structure
of such algebras. As an application, we prove a number of results on the existence of invariant subspaces for algebraic structures
of compact operators, in particular for Jordan algebras and Lie triple systems of Volterra operators. Along the way we obtain
new criteria for the triangularizability of a Lie algebra of compact operators.
The support received from INTAS project No 06-1000017-8609 is gratefully acknowledged by the third author. 相似文献
3.
Ian M. Musson 《代数通讯》2013,41(10):3759-3777
If is a semisimple Lie algebra, we describe the prime factors of () that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also determine, which finite dimensional ()-modules are modules over a given prime factor. As an application we study finite dimensional modules over some rings of invariant differential operators arising from Howe duality. 相似文献
4.
Miron B. Bekker 《Complex Analysis and Operator Theory》2009,3(3):587-610
We consider isometric operators with finite defect numbers that are unitarily equivalent to their M?bius transformations.
A functional characterization of such isometries is given in terms of their characteristic operator-functions. We show that
any such isometry admits a contractive extension that is also unitarily equivalent to its M?bius transformation and a unitary
extension in a larger space that has the same property. Examples of automorphic invariant operators are considered. 相似文献
5.
Yasusi Hasimoto 《Mathematical Logic Quarterly》2001,47(2):187-196
6.
P.T. ChurchJ.G. Timourian 《Journal of Differential Equations》2002,181(2):463-510
There is an increasing literature devoted to the study of boundary value problems using singularity theory. The resulting differential operators are typically Fredholm with index 0, defined on infinite-dimensional spaces, and they have often led to folds, cusps, and even higher-order Morin singularities. In this paper we develop some of the local algebras of germs of such differential Fredholm operators, extending the theory of the finite-dimensional case. We apply this work to nonlinear elliptic boundary value problems: in particular, we make further progress on a question proposed and initially studied by Ruf [1999, J. Differential Equations 151, 111-133]. We also make comments on several problems raised by others. 相似文献
7.
Sheila Brenner Michael C. R. Butler Alastair D. King 《Algebras and Representation Theory》2002,5(4):331-368
The preprojective algebra and the trivial extension algebra of a Dynkin quiver (in bipartite orientation) are very close to being a Koszul dual pair of algebras. In this case the usual duality theory may be adapted to show that each algebra has a periodic bimodule resolution built using the other algebra and some extra data: an algebra automorphism. A general theory of such almost Koszul algebras is developed and other examples are given. 相似文献
8.
Invariant Lie Algebras and Lie Algebras with a Small Centroid 总被引:1,自引:0,他引:1
K. N. Ponomaryov 《Algebra and Logic》2001,40(6):365-377
A subalgebra of a Lie algebra is said to be invariant if it is invariant under the action of some Cartan subalgebra of that algebra. A known theorem of Melville says that a nilpotent invariant subalgebra of a finite-dimensional semisimple complex Lie algebra has a small centroid. The notion of a Lie algebra with small centroid extends to a class of all finite-dimensional algebras. For finite-dimensional algebras of zero characteristic with semisimple derivations in a sufficiently broad class, their centroid is proved small. As a consequence, it turns out that every invariant subalgebra of a finite-dimensional reductive Lie algebra over an arbitrary definition field of zero characteristic has a small centroid. 相似文献
9.
10.
11.
In ([11]), we have studied quadratic Leibniz algebras that are Leibniz algebras endowed with symmetric, nondegenerate, and associative (or invariant) bilinear forms. The nonanticommutativity of the Leibniz product gives rise to other types of invariance for a bilinear form defined on a Leibniz algebra: the left invariance, the right invariance. In this article, we study the structure of Leibniz algebras endowed with nondegenerate, symmetric, and left (resp. right) invariant bilinear forms. In particular, the existence of such a bilinear form on a Leibniz algebra 𝔏 gives rise to a new algebra structure ☆ on the underlying vector space 𝔏. In this article, we study this new algebra, and we give information on the structure of this type of algebras by using some extensions introduced in [11]. In particular, we improve the results obtained in [22]. 相似文献
12.
We explore a connection between different ways of representing information in computer science. We show that relational databases,
modules, algebraic specifications and constraint systems all satisfy the same ten axioms. A commutative semigroup together
with a lattice satisfying these axioms is then called an “information algebra”. We show that any compact consequence operator
satisfying the interpolation and the deduction property induces an information algebra. Conversely, each finitary information
algebra can be obtained from a consequence operator in this way. Finally we show that arbitrary (not necessarily finitary)
information algebras can be represented as some kind of abstract relational database called a tuple system.
Mathematics Subject Classification (2000): Primary 03B22; Secondary 03G15 03G25 08A70 68Q99 94A99 03C950 相似文献
13.
In this paper, the continuity of consequence operators is introduced. Relations between consequence operators and their associated information algebras are mainly explored. It is shown that, for any given consequence operator, the associated information algebra can be directly constructed without any additional conditions.Furthermore, if the consequence operators are continous or compact, then the associated information algebras are continuous or compact. 相似文献
14.
Russian Mathematics - We study finite-dimensional Lie algebras which have a codimension one abelian ideal and prove some their properties including those related to the structure of the space of... 相似文献
15.
一类不变的Hankel算子 总被引:3,自引:0,他引:3
对于La,2(D)的两类Moebius不变子空间Ala,2(D)与Al-a,2(D),定义了对解析的记号函数b(z)的大的和小的Hankel算子Hbll′与hbll′,研究了它们的有界性、紧性及其Schatten-von Neumann类的SP估计.性质。 相似文献
16.
Periodica Mathematica Hungarica - 相似文献
17.
W. Timmermann 《Mathematische Nachrichten》1979,92(1):99-110
A general procedure is given to get ideals in algebras of unbounded operators starting with ideals in ??(??). Algebraical and topological properties of ideals obtained in this manner from the well-known symmetrically-normed ideals S?(??) are described. 相似文献
18.
19.
David A. Richter 《Acta Appl Math》2001,66(1):41-65
Starting from the commutation relations in a complex semisimple Lie algebra
, one may obtain a space
of vector fields on Euclidean space such that
and
are isomorphic when
is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of
is a Borel subalgebra
. Furthermore, one may adjoin to the vector fields in
multiplication operators to obtain an
-parameter family of distinct presentations of
as spaces of differential operators, where
is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of
can be presented in this way. All of this is carried out explicitly for arbitrary
. In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight. 相似文献
20.
刘明学 《应用泛函分析学报》2000,2(4):328-330
证明关于压缩算子的如下不变子空间定理:如果T是Hilbert空间H上的压缩算子,且集合Z’={λ∈D;存在z∈H,使得‖z‖=1,且‖(λ-T)z‖<1/3(1-‖λ‖}是开单位圆D的控制集,那么T有非平凡的不变子空间,这个定理包含了S.Brown,B.Chevreau,C.fPearcy和B.Beauzamy的两个重要结果作为特殊情况,特别是,为个定理包含了S.Brown等人的Hilbert空间上的每个具有厚谱的压缩算子都有平凡的不变子空间这个重要结果作为特殊情况。 相似文献