L-偏序集中L_k-素闭包算子和L_k-素内部算子

本文在完备剩余格上引入了L-偏序集,给出了L-偏序集上L_k-素闭包算子和L_k-素内部算子的概念及其等价刻画,在此基础上推广得出了n重L_k-素闭包算子和n重L_k-素内部算子的概念及其等价刻画。     

向量值弱BMO空间上鞅均方算子的有界性

证明了X同构于q一致凸Banach空间的充分必要条件是,鞅的q阶均方算子S~((q))(·)是(ωBMO_q~α(X),ωBMO_q~α(R))型的和(L_q(X),ωBMO_q~α(R))型的.所得结果给出了Banach空间的q一致凸性的新等价刻画形式.     

模糊粗糙近似算子的拓扑性质

考虑论域上一二元关系所决定的模糊粗糙近似算子的拓扑性质,证明了任一自反二元关系可以决定一模糊拓扑.并且,当二元关系自反对称时,该模糊拓扑中的元是开集当且仅当它是闭集;当二元关系自反传递时,该模糊拓扑的闭包与内部算子恰为模糊粗糙上、下近似算子.     

关于L—fuzzy拓扑空间的闭包算子与乘积算子的可交换性

本文利用Fuzzy格的代数性质,从L-fuzzy拓扑的层次结,构入手,定义了闭包保层空间,藉助于它给出了满层L-fuzzy拓扑空间的闭包算子与乘积算子可交换的等价条件,并证明了:若乘积L-fuzzy拓扑空间的每个因子空间都是诱导的,则闭包算子与乘积算子是可交换的,从而较好地解决了[2]中所提出的问题。     

(L,M)-fuzzy闭包系统与(L,M)-fuzzy闭包算子

定义了(L,M)-fuzzy闭包系统与(L,M)-fuzzy闭包算子的概念,建立了给定集合X上(L,M)-fuzzy闭包系统的全体FCS(L,M,X)和(L,M)-fuzzy闭包算子的全体FCO(L,M,X)之间的一一对应(在此基础上证明了(L,M)-fuzzy闭包系统空间范畴LMFCSS与(L,M)-fuzzy闭包算子空间范畴LMFCOS是同构的)。此外还证明了(2,M)-fuzzy闭包系统空间范畴2MFCSS可嵌入到(L,M)-fuzzy闭包系统空间范畴LMFCSS,(2,M)-fuzzy闭包算子空间范畴2MFCOS可嵌入到(L,M)-fuzzy闭包算子空间范畴LMFCOS。     

Toeplitz算子空间的W—闭包

本文讨论了Ｔｏｅｐｌｉｔｚ算子空间的Ｗ－闭包，我们证明了Ｂｅｒｇｍａｎ空间Ｌ＾２ａ（Ｄ）上全体Ｔｏｅｐｌｉｔｚ算子的Ｗ闭包等于Ｂ（Ｌ＾２ａ（Ｄ）（定理１），另外，我们给出Ｃ＾ｍ（ｎ＞１）中单位球面Ｓ上的Ｈａｒｄｙ空间Ｈ＾２（Ｓ）上的Ｔｏｅｐｌｉｔｚ算子的一个有趣刻划（命题２）。     

Riemann曲面上的正常和拟正常复合算子

Riemann曲面M上的平方可测1-形式全体和解析1-形式全体均可构成Hilbert空间.本文讨论Riemann曲面上的解析映射导出的这类Hilbert空间上的复合算子,研究复合算子的正常性、拟正常性的诱导映射特征.特别地,当M有有限三角剖分时,证明了正常复合算子、拟正常复合算子、酉复合算子、等距复合算子和可逆复合算子等价.     

有限格，闭包系统和闭包算子

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.     

Bergman空间上Toeplitz算子的凸性

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的凸性，证明了具有调和符号和一类连续函数符号的Ｔｏｅｐｌｉｔｚ算子是凸型算子，并举例说明，存在具有连续函数符号的非凸型Ｔｏｅｐｌｉｔｚ算子。     

Toeplitz算子空间的ω~＊－闭包

本文讨论Ｔｏｅｐｌｉｔｚ算子空间的ω￣＊－闭包．我们证明Ｂｅｒｇｍａｎ空间上全体Ｔｏｅｐｌｉｔｚ算子的ω￣＊－闭包等于（定理１）．另外，我们给出Ｃ￣ｎ（ｎ＞１）中单位球面Ｓ上的Ｈａｒｄｙ空间Ｈ￣２（Ｓ）上的Ｔｏｅｐｌｉｔｚ算子的一个有趣刻划（命题２）．     

Averaged Wave Operators and Complex-symmetric Operators

We study the behaviour of sequences \(U_2^n X U_1^{-n}\), where \(U_1, U_2\) are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator \(XU_1-U_2X\) is small in a sense. The conjecture about the weak averaged convergence of the difference \(U_2^n X U_1^{-n}-U_2^{-n} X U_1^n\) to the zero operator is discussed and its connection with complex-symmetric operators is established in a general situation. For a model case where \(U_1=U_2\) is the unitary operator of multiplication by z on \(L^2(\mu )\), sufficient conditions for the convergence as in the Conjecture are given in terms of kernels of integral operators.     

Continuity of Operators Intertwining with Convolution Operators

Let G be a locally compact abelian group, let μ be a bounded complex-valued Borel measure on G, and let T_μ be the corresponding convolution operator on L¹(G). Let X be a Banach space and let S be a continuous linear operator on X. Then we show that every linear operator Φ: X→L¹(G) such that ΦS=T_μΦ is continuous if and only if the pair (S,T_μ) has no critical eigenvalue.     

算子的拟相似与(Q)类算子

本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.     

Pseudodifferential Operators Associated with a Semigroup of Operators

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L ^p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class $S^{0}_{1,\delta}$ for δ∈[0,1). For the limit class $S^{0}_{1,1}$ , we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.     

亚超循环算子与可逆算子的亚超循环性

设X为无限维可分的Banach空间,T是X上的有界线性算子.利用轨道C·Orb(x,T)的d稠密性给出了T是亚超循环算子的充分条件.此外,还考虑可逆的亚超循环算子T并从循环向量的角度刻画了T和T~(-1)的亚超循环性.     

p-Dirac Operators

We introduce non-linear Dirac operators in associated to the p-harmonic equation and we extend to other contexts including spin manifolds and the sphere. This paper is dedicated to the memory of Jarolim Bureš Received: October, 2007. Accepted: February, 2008.     

单调算子和强制算子的相补问题

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。     

S-Storage Operators

In 1990, J. L. Krivine introduced the notion of storage operator to simulate, for Church integers, the “call by value” in a context of a “call by name” strategy. In the present paper we define for every λ-term S which realizes the successor function on Church integers the notion of S-storage operator. We prove that every storage operator is an S-storage operator. But the converse is not always true.