广义Kato分解与拓扑一致降指数

讨论了算子的广义Kato分解与拓扑一致降指数,给出算子既有广义Kato分解又有拓扑一致降指数的等价刻画,并由此对算子谱精细结构进行进一步的细化.     

广义Kato分解与Weyl型定理的摄动

称T∈B(H)有广义Kato分解,若存在一对T的闭的不变子空间(M,N)使得H=M⊕Ⅳ,其中T|_M为上半Fredholm算子且具有非负的指标,T|_N是幂零的本文利用算子的广义Kato分解性质,研究了Weyl型定理在紧摄动下的稳定性.此外还研究了2×2上三角算子矩阵的Weyl型定理在紧摄动下的稳定性.     

算子矩阵的亚循环性

讨论了亚循环算子和具有拓扑一致降标的算子之间的关系,同时研究了算子矩阵的亚循环性和超循环性.     

一致可逆性质及广义(ω)性质的摄动

Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H),TS与ST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性.     

正定自伴算子分数幂的泛函不等式

本文研究了super-Poincaré不等式在变换下的稳定性.利用自伴算子的谱分解性质,证明了当正定自伴算子L满足super-Poincaré不等式时,L的分数幂Lα也满足相应的super-Poincaré不等式,并讨论了相应半群的几种超有界性之间的关系.     

J-次正常算子的不变子空间

本文证明n阶J-次正常算子在一个亏维数不超过n的不变子空间的限制是次正常算子,且当n>O时这类算子有非平凡超不变子空间。由此易知J-次正常算子有非平凡不变子空间。我们还讨论了拟幂零的和紧的J-次正常算子。     

(h)性质的一个新刻画（英文）

本文利用广义Kato性质诱导的谱集,研究了Weyl定理的一种新变形,称其为(h)性质,并证明了(h)性质如何根据该谱集性质得到.同时给出了直和算子T⊕S满足(h)性质的条件.此外,利用该诱导谱集研究了Banach空间上的有界算子T在与T交换的幂有限秩算子扰动下的(h)性质稳定性.     

三种形式的Putnam-Fuglede定理的等价性以及有关结果

本文讨论了Hilbert空间的算子论中的三种形式的 Putnam-Fuglede定理的等价性。证明了一对算子的正规性和亚正规性的关于Hilbert-Schmidt范数‖·‖_2的一些特征,并给出一些在拟幂零扰动下的 Putnam-Fuglede型定理。     

对性质(ω)等价性的研究

性质(ω)是Weyl定理的一种变形.文章中将算子的一致Fredholm指标性质用于性质(ω)的判定中.根据一致Fredholm指标性质定义出一种新的谱集,通过该谱集和算子的拓扑一致降标之间的关系,给出了有界线性算子与其共轭算子同时满足性质(ω)的充要条件.之后,研究了算子矩阵的(ω)性质.     

广义Kato分解与(ω)性质的稳定性判定

研究Hilbert空间上有界线性算子的(ω)性质,给出了广义Kato型的定义并根据广义Kato型的性质定义了一种新的谱集,利用该谱集给出了Hilbert空间上有界线性算子满足(ω)性质的充要条件,并且讨论了(ω)性质的稳定性.     

Algebraic K-theory of non-linear projective spaces

In the spirit of “The Fundamental Theorem for the algebraic K-theory of spaces: I” (J. Pure Appl. Algebra 160 (2001) 21–52) we introduce a category of sheaves of topological spaces on n-dimensional projective space and present a calculation of its K-theory, a “non-linear” analogue of Quillen's isomorphism K_i(P_Rⁿ)₀ⁿK_i(R).     

Families of operators satisfying relations

A problem of unitary classification of families of operators R_i= R _i ^* =R_i/–1 in a Hilbert space, connected by some additional relations. Such families occur in problems concerning representations of a side class of *-algebras, among others, two parameter deformations U(su (2)), constructed by E. K. Sklyannyi.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 309–317, March, 1992.     

Asymptotic joint distribution of the largest roots of several multivariate F matrices I. Quasi-independent case

An asymptotic expansion of the joint distribution of k largest characteristic roots C_M⁽ⁱ⁾(S_iS₀^?1), i = 1,…, k, is given, where S'_is and S₀ are independent Wishart matrices with common covariance matrix Σ. The modified second-approximation procedure to the upper percentage points of the maximum of C_M⁽ⁱ⁾(S_iS₀^?1), i = 1,…, k, is also considered. The evaluation of the expansion is based on the idea for studentization due to Welch and James with the use of differential operators and of the perturbation procedure.     

Weak Limits for Multivariate Random Sums

Let {Xi, i1} be a sequence of i.i.d. random vectors inRd, and letνp, 0<p<1, be a positive, integer valued random variable, independent ofXis. Theν-stable distributions are the weak limits of properly normalized random sums ∑νpi=1 Xiasνp ∞ andpνp ν. We study the properties ofν-stable laws through their representation via stable laws. In particular, we estimate their tail probabilities and provide conditions for finiteness of their moments.     

Topological uniform descent and Weyl type theorem

The generalized Weyl’s theorem holds for a Banach space operator T if and only if T or T^∗ has the single valued extension property in the complement of the Weyl spectrum (or B-Weyl spectrum) and T has topological uniform descent at all λ which are isolated eigenvalues of T. Also, we show that the generalized Weyl’s theorem holds for analytically paranormal operators.     

Quotient-reflective and bireflective subcategories of the category of preordered sets

In previous papers, the notions of “closedness” and “strong closedness” in set-based topological categories were introduced. In this paper, we give the characterization of closed and strongly closed subobjects of an object in the category Prord of preordered sets and show that they form appropriate closure operators which enjoy the basic properties like idempotency (weak) hereditariness, and productivity.We investigate the relationships between these closure operators and the well-known ones, the up- and down-closures. As a consequence, we characterize each of T₀, T₁, and T₂ preordered sets and show that each of the full subcategories of each of T₀, T₁, T₂ preordered sets is quotient-reflective in Prord. Furthermore, we give the characterization of each of pre-Hausdorff preordered sets and zero-dimensional preordered sets, and show that there is an isomorphism of the full subcategory of zero-dimensional preordered sets and the full subcategory of pre-Hausdorff preordered sets. Finally, we show that both of these subcategories are bireflective in Prord.     

Valuations, equimultiplicity and normal flatness

Let R be a regular noetherian local ring of dimension n≥2 and (R_i)≡R=R₀⊂R₁⊂R₂⊂?⊂R_i⊂? be a sequence of successive quadratic transforms along a regular prime ideal p of R (i.e if p_i is the strict transform of p in R_i, then p_i≠R_i, i≥0). We say that p is maximal for (R_i) if for every non-negative integer j≥0 and for every prime ideal q_j of R_j such that (R_i) is a quadratic sequence along q_j with p_j⊂q_j, we have p_j=q_j. We show that p is maximal for (R_i) if and only if V=∪_i≥0R_i/p_i is a valuation ring of dimension one. In this case, the equimultiple locus at p is the set of elements of the maximal ideal of R for which the multiplicity is stable along the sequence (R_i), provided that the series of real numbers given by the multiplicity sequence associated with V diverges. Furthermore, if we consider an ideal J of R, we also show that is normally flat along at the closed point if and only if the Hironaka’s character ν^∗(J,R) is stable along the sequence (R_i). This generalizes well known results for the case where p has height one (see [B.M. Bennett, On the characteristic functions of a local ring, Ann. of Math. Second Series 91 (1) (1970) 25-87]).     

The Taylor–Browder Spectrum on Prime C*-Algebras

We provide a formula for the Taylor–Browder spectrum of a pair (L _a , R _b ) of left and right multiplication operators acting on a prime C*-algebra with non-zero socle. We also compute ascent and descent for multiplication operators on a prime ring, characterise Browder elements in a prime C*-algebra and discuss upper semicontinuity for the Browder spectrum.