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1.
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   

2.
An operator F ∈ B(X) is called power finite rank if F~n is of finite rank for some n ∈ N.In this note, we provide several interesting characterizations of power finite rank operators. In particular, we show that the class of power finite rank operators is the intersection of the class of Riesz operators and the class of operators with eventual topological uniform descent.  相似文献   

3.
由扭算子构成的扭算子李代数在李代数理论中占有重要的位置,首先构造了一般形式的扭顶点算子Z~σ(E_(ij),α,β,z),然后给出了一般扭算子李代数g(G,l)[σ],研究了一般扭顶点算子所具有的性质.  相似文献   

4.
《代数通讯》2013,41(3):1485-1497
Abstract

We define the lower socle of a semiprime algebra 𝒜 as the sum of all minimal left ideals 𝒜e where e is a minimal idempotent such that the division algebra e𝒜e is finite dimensional. We study the connection between the condition that the elements a k , b k , 1 ≤ k ≤ n, lie in the lower socle of 𝒜 and the condition that the elementary operator x ? a 1 xb 1 + ? + a n xb n has finite rank. As an application we obtain some results on derivations certain of whose powers have finite rank.  相似文献   

5.
获得了Bergman空间上形如(T_f,T_g]-T_(h~n)和[T_f,T_g]-T_(h~n)的算子为有限秩时的充要条件,其中f,g,h均为有界调和函数,n为非负自然数.  相似文献   

6.
Finiterankoperatorsandrankoneoperatorsareimportanttothetheoryofnestalgebras .Inanestalgebra ,eachfiniterankoperatorcanbewrittenasafinitesumofrankoneoperatorswhichbelongtoitself (Thisresultisin [1 ],butbelongstoJ .R .Ringrose) .Inanaturalway ,wemayask : Question…  相似文献   

7.
设F是一个域,a∈F~nF~m.若存在h∈F~m,k∈F~m,使得a=hk,则称a是可分的.空间F~nF~m上的线性算子A称为是强可分的,是指x∈F~nF~m,x可分Ax可分.本文证明了F~nF~n上的线性算子A是强可分的当且仅当存在F~n上的线性双射A_1与A_2,使得A=A_1A_2或A=A_1~T A_2;证明了F~nF~m(n≠m)上线性算子A是强可分的当且仅当存在F~n与F~m上的线性双射A_1与A_2,使得A=A_1A_2.最后,给出了可分算子、强可分算子和秩1保持映射之间的关系.  相似文献   

8.
本文引进了新的闭包系统,新的闭包算子等概念,研究了它们之间的相互关系,给出了由闭包系统来表示有限原子格的表示定理,证明了分别以这些数学结构为对象,以它们之间的同态映射作为态射,所对应的格范畴和对应的闭包系统范畴是范畴等价的.  相似文献   

9.
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   

10.
双参数有限q指数算子及其应用   总被引:1,自引:0,他引:1  
张之正  杨继真 《数学学报》2010,53(5):1007-1018
本文构造两个双参数有限q指数算子,得到了几个算子恒等式;应用这些算子恒等式到著名的q-Chu-Vandermonde求和恒等式,求导了若干奇异的q-级数恒等式,包含著名的Jackson恒等式的一个推广.  相似文献   

11.
In this paper functional completeness results are obtained for certain positive and constructive propositional logics associated with a Tarski-type structured consequence relation as defined by Gabbay.  相似文献   

12.
Ignat'ev  M. Yu. 《Mathematical Notes》2003,73(1-2):192-201
We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.  相似文献   

13.
This paper is primarily concerned with the problem of maximality for the sum A + B and composition L* ML in non-reflexive Banach space settings under qualifications constraints involving the domains of A, B, M. Here X, Y are Banach spaces with duals X*, Y*, A, B: XX*, M: YY* are multi-valued maximal monotone operators, and L: XY is linear bounded. Based on the Fitzpatrick function, new characterizations for the maximality of an operator as well as simpler proofs, improvements of previously known results, and several new results on the topic are presented.   相似文献   

14.
In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.  相似文献   

15.
We study a finite element approximation A h, based on simplicial Lagrange elements, of a second order elliptic operator A under homogeneous Dirichlet boundary conditions in two and three dimensions, where h is thought of as a meshsize. The main result of the paper is a new resolvent estimate for the operator A h in the L -norm. This estimate is uniform with respect to h for the case with at least quadratic elements. In the case with linear elements, the estimate contains on the right a factor proportional to (log log ), where = 1 or = in two or three dimensions, respectively.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

16.
Operator Matrix Forms of Positive Operators   总被引:2,自引:0,他引:2  
If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2)of operators on Hibert spaces is given,we proved that the operator ~↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R(A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet.  相似文献   

17.
单调算子和强制算子的相补问题   总被引:1,自引:0,他引:1  
讨论了单调算子和强制算子的相补问题,给出了解的存在性定理。并进一步证明了严格单调算子的解的唯一定理。  相似文献   

18.
19.
本文研究了调和Bergman空间上的Toeplitz的Brown-Halmos型零乘积问题以及有限秩的相关性质,并得到了以解析和余解析符号的Toeplitz算子乘积的有限和的零积有限秩的等价条件.  相似文献   

20.
纪友清  王春梅 《数学学报》2007,50(4):775-780
本文证明了H~p(T)(1≤p≤∞)空间上以n阶Blaschke乘积为符号的Toeplitz算子相似于⊕_nT_z,从而证明了这类算子的有限BIR分解在相似下唯一.  相似文献   

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