共查询到20条相似文献,搜索用时 15 毫秒
1.
The notion of an alternatingly hyperexpansive operator on a Hilbert space is generalized to that of an alternatingly hyperexpansive operator tuple, which necessitates exploring the theory of absolutely monotone functions as defined on the m-fold product N
m of the semi-group N of non-negative integers and as defined on semi-open cubes in the m-dimensional real Euclidean space R
m. The multi-variable Laplace transform and the Stieltjes Moment Problem make a natural appearance in the development of the relevant theory, which also highlights the close connections of alternatingly hyperexpansive operator tuples with completely hyperexpansive and subnormal ones. In particular, if T is subnormal and the joint (Taylor) spectrum of its minimal normal extension is contained in a certain subset of the Hermitian space C
m, then T turns out to be alternatingly hyperexpansive. In the context of multi-variable weighted shifts, the last assertion can be related to the notion of a Stieltjes Moment Net. The general characterization of an alternatingly hyperexpansive m-variable weighted shift T, however, requires a certain net of (positive) numbers associated with T to be absolutely monotone on N
m and allows for such a T to be non-subnormal. 相似文献
2.
Ameer Athavale 《Proceedings of the American Mathematical Society》1996,124(12):3745-3752
We introduce and discuss a class of operators, to be referred to as the class of completely hyperexpansive operators, which is in some sense antithetical to the class of contractive subnormals. The new class is intimately related to the theory of negative definite functions on abelian semigroups. The known interplay between positive and negative definite functions from the theory of harmonic analysis on semigroups can be exploited to reveal some interesting connections between subnormals and completely hyperexpansive operators.
3.
Zenon J. Jaboski 《Integral Equations and Operator Theory》2002,44(3):316-336
Athavale introduced in [3] the notion of a completely hyperexpansive operator. In this paper some results concerning powers of completely (alternatingly) hyperexpansive operators (not necessarily bounded) are extended tok-hyperexpansive ones. A semispectral measure is associated with a subnormal contraction as well as with a completely hyperexpansive operator, and an operator version of the Levy-Khinchin representation is obtained. Passing to the Naimark dilation of the semispectral measure, such an operator is related to a positive contraction in a natural way. New characterizations of a completely hyperexpansive operator and a subnormal contraction are given. The power bounded completely hyperexpansive operators are characterized. All these are illustrated using weighted shifts. 相似文献
4.
Wen-Bin Zhang 《The Ramanujan Journal》2002,6(4):387-428
We extend the investigation of quantitative mean-value theorems of completely multiplicative functions on additive arithmetic semigroups given in our previous paper. Then the new and old quantitative mean-value theorems are applied to the investigation of local distribution of values of a special additive function *(a). The result is unexpected from the point of view of classical number theory. This reveals the fact that the essential divergence of the theory of additive arithmetic semigroups from classical number theory is not related to the existence of a zero of the zeta function Z(y) at y = –q
–1. 相似文献
5.
Multivariable Bernstein functions are used to discover some interesting connections between multivariable completely hyperexpansive weighed shifts and multivariable subnormal weighted shifts. 相似文献
6.
Special classes of functions on the classical semigroupN of non-negative integers, as defined using the classical backward and forward difference operators, get associated in a natural way with special classes of bounded linear operators on Hilbert spaces. In particular, the class of completely monotone functions, which is a subclass of the class of positive definite functions ofN, gets associated with subnormal operators, and the class of completely alternating functions, which is a subclass of the class of negative definite functions onN, with completely hyper-expansive operators. The interplay between the theories of completely monotone and completely alternating functions has previously been exploited to unravel some interesting connections between subnormals and completely hyperexpansive operators. For example, it is known that a completely hyperexpansive weighted shift with the weight sequence {n}(n0) (of positive reals) gives rise to a subnormal weighted shift whose weight sequence is {1/n}(n0). The present paper discovers some new connections between the two classes of operators by building upon some well-known results in the literature that relate positive and negative definite functions on cartesian products of arbitrary sets using Bernstein functions. In particular, it is observed that the weight sequence of a completely hyperexpansive weighted shift with the weight sequence {n}(n0) (of positive reals) gives rise to a subnormal weighted shift whose weight sequence is {n+1/n}(n0). It is also established that the weight sequence of any completely hyperexpansive weighted shift is a Hausdorff moment sequence. Further, the connection of Bernstein functions with Stieltjes functions and generalizations thereof is exploited to link certain classes of subnormal weighted shifts to completely hyperexpansive ones. 相似文献
7.
Torben Maack Bisgaard 《Czechoslovak Mathematical Journal》2002,52(1):155-196
We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters). 相似文献
8.
Ameer Athavale 《Integral Equations and Operator Theory》1989,12(3):305-323
A notion of the dual of a subnormal tuple of operators is discussed. 相似文献
9.
In this paper,fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets.Furthermore,we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals.Finally,we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals. 相似文献
10.
利用Crandall—Liggett半群定理和完全增长算子的性质,得到初始值属于L^2(Ω)的极小变分流第二边值问题弱解的存在性. 相似文献
11.
Truncations of completely alternating sequences are entirely characterized. The completely hyperexpansive completion problem is solved for finite sequences of (positive) numbers in terms of positivity of attached matrices. Solutions to the problem are written explicitly for sequences of two, three, four, five and six numbers. As an application, an explicit solution of the subnormal completion problem for five numbers is given. 相似文献
12.
13.
Yoshikazu Kobayashi Toshitaka Matsumoto Naoki Tanaka 《Journal of Mathematical Analysis and Applications》2007,330(2):1042-1067
In this paper we introduce the notion of semigroups of locally Lipschitz operators which provide us with mild solutions to the Cauchy problem for semilinear evolution equations, and characterize such semigroups of locally Lipschitz operators. This notion of the semigroups is derived from the well-posedness concept of the initial-boundary value problem for differential equations whose solution operators are not quasi-contractive even in a local sense but locally Lipschitz continuous with respect to their initial data. The result obtained is applied to the initial-boundary value problem for the complex Ginzburg–Landau equation. 相似文献
14.
15.
O. Yu. Dashkova 《Ukrainian Mathematical Journal》1995,47(11):1801-1805
We introduce the notion of subnormal rank of a group and study hypercentral groups of finite subnormal rank. We construct an example of a hypercentral group that has a finite subnormal rank and infinite (special) rank.Translated from Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 11, pp. 1577–1580, November, 1995. 相似文献
16.
Certain Partial Orders on Semigroups 总被引:1,自引:0,他引:1
Mario Petrich 《Czechoslovak Mathematical Journal》2001,51(2):415-432
Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups. 相似文献
17.
The structure of superabundant semigroups 总被引:9,自引:0,他引:9
K.P.Shum 《中国科学A辑(英文版)》2004,47(5):756-771
A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened. 相似文献
18.
Jörg Eschmeier 《Integral Equations and Operator Theory》2007,59(2):165-172
The question whether every subnormal tuple
on a complex Hilbert space is reflexive is one of the major open problems in multivariable invariant subspace theory. Positive
answers have been given for subnormal tuples with rich spectrum in the unit polydisc or the unit ball. The ball case has been
extended by Didas [6] to strictly pseudoconvex domains. In the present note we extend the polydisc case by showing that every
subnormal tuple with pure components and rich Taylor spectrum in a bounded polydomain
is reflexive. 相似文献
19.
B. V. Rajarama Bhat Tirthankar Bhattacharyya Santanu Dey 《Transactions of the American Mathematical Society》2004,356(4):1551-1568
We introduce a notion called `maximal commuting piece' for tuples of Hilbert space operators. Given a commuting tuple of operators forming a row contraction, there are two commonly used dilations in multivariable operator theory. First there is the minimal isometric dilation consisting of isometries with orthogonal ranges, and hence it is a noncommuting tuple. There is also a commuting dilation related with a standard commuting tuple on boson Fock space. We show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation. We use this result to classify all representations of the Cuntz algebra coming from dilations of commuting tuples.
20.
We introduce the notion of (joint) formal normality for a collection of unbounded linear operators on a separable Hilbert
space H which is, in some sense, a natural generalization of the notion of formal normality for a single operator. We give some relations
between this new notion and (joint) subnormality and hyponormality. We adapt, in particular, a proof of Stochel and Szafraniec
to give necessary and sufficient conditions for a tupleof unbounded operators with invariant domain to be (jointly) subnormal. 相似文献