Composition and Multiplication Operators on L^(p,∞)(M)

We give some properties of the composition and multiplication operators on L^(p,∞)(M), where M is a semifinite von Neumann algebra with a normal semifinite faithful trace τ.

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

In this article, we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.

Boundedness of Multiplication Operators on α-Bloch Spaces

In this note we study and give a full characterization of the boundeness of mul-tiplication operators on α-Bloch spaces.

Reducing subspaces of multiplication operators with the symbol αz^k+ βw^l on L_a^2(D^2)

Multiplication operators defined on function spaces have been receiving enormous attention from both operator-theoretic and function-theoretic experts. One of the problems is to study reducing subspaces of them. The one-variable case has obtained fruitful remarkable results. However, little has been done in the multi-variable case. Under the setting of the Bergman space L2a(D2), this paper addresses those multiplication operators Mp defined by special polynomials p, where p(z, w) = αzk+ βwl, α, β∈ C. Those reducing subspaces of Mp are completely determined.

Finite Blaschke product and the multiplication operators on Sobolev disk algebra

Let R(D) be the algebra generated in Sobolev space W 22(D) by the rational functions with poles outside the unit disk $ \overline D $ . In this paper the multiplication operators M g on R(D) is studied and it is proved that M g ～ $ M_{z^n } $ if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then M g has uncountably many Banach reducing subspaces if and only if n > 1.

Normality Preserving Multiplication Operators

We show that a multiplication operator Φ(T)=ATB is normality preserving if and only if it is hyponormality preserving,if and only if it is either of the form A=f(?)g,B=h(?)f, or A=D,B=λD~* for some λ∈C and D E B(H) with D~*D=I.Also we show that Φ is(semi-) Fredholmness prserving if and only if A and B are(semi-)Fredholm operators.

Reducing problem of multiplication operators on Bergman space

THE L_a^2(D) refers to Bergman space on D, where D is the unit disk on the complex plane. Using the super-isometric dilation technique, we obtain the following results. Proposition 1. The multiplication operator M_φ on Bergman space L_a^2 (D) is unitarily equivalent to the compression of the direct sum of 2N-1 copies of Bergman shift, where φ is a Blaschke product of order N (【∞).

Hardy-Orlicz Spaces and Their Multiplication Operators

In this paper some formulae on the relationship between Hardy and Hardy Orlicz spaces are presented, and multiplication operators on Hardy-Orlicz spaces are discussed.

Similarity of Multiplication Operators on the Sobolev Disk Algebra

Abstract In this paper, we give a similarity classification for the multiplication operator Mg on the Sobolev disk algebra R（D） with g analytic on the closure of the unit disk D.

ON F(p,q,s)SPACES

The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.

Flexibility of MIP Technology

The flexibility of MIP technology to meet market demand is mainly introduced in this study. Their commercial application and technical principle are analyzed too. The MIP technology with wide feed adaptability can form a good combination with other technologies. The MIP technology has been applied extensively in China. Based on this platform, the CGP, MIP-LTG and MIP-DCR technologies have been developed, which can further improve the flexibility of MIP technology. Based on its novel reaction control technique with a sole sequential two-zone riser, the MIP users can easily switch to different operating modes between producing either more clean gasoline and propylene or diesel through changing the catalysts and varying the operating conditions. That offers MIP users with enough production flexibility and a rational production arrangement to meet the market demand. The MIP-DCR technology with less dry gas and coke yields can provide a more flexible operating mode since the catalysts to oil ratio has become an independent variable.

Multi-mode process monitoring based on a novel weighted local standardization strategy and support vector data description

There are multiple operating modes in the real industrial process, and the collected data follow the complex multimodal distribution, so most traditional process monitoring methods are no longer applicable because their presumptions are that sampled-data should obey the single Gaussian distribution or non-Gaussian distribution. In order to solve these problems, a novel weighted local standardization(WLS) strategy is proposed to standardize the multimodal data, which can eliminate the multi-mode characteristics of the collected data, and normalize them into unimodal data distribution. After detailed analysis of the raised data preprocessing strategy, a new algorithm using WLS strategy with support vector data description(SVDD) is put forward to apply for multi-mode monitoring process. Unlike the strategy of building multiple local models, the developed method only contains a model without the prior knowledge of multi-mode process. To demonstrate the proposed method's validity, it is applied to a numerical example and a Tennessee Eastman(TE) process. Finally, the simulation results show that the WLS strategy is very effective to standardize multimodal data, and the WLS-SVDD monitoring method has great advantages over the traditional SVDD and PCA combined with a local standardization strategy(LNS-PCA) in multi-mode process monitoring.

UNIVERSAL INTERPOLATING SEQUENCES ON SPACES OF ANALYTIC FUNCTIONS

This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.

Dual-radiation-chamber coordinated overall energy efficiency scheduling solution for ethylene cracking process regarding multi-parameter setting and multi-flow allocation

Ethylene cracking process is the core production process in ethylene industry,and is paid more attention to reduce high energy consumption.Because of the interdependent relationships between multi-flow allocation and multi-parameter setting in cracking process,it is difficult to find the overall energy efficiency scheduling for the purpose of saving energy.The traditional scheduling solutions with optimal economic benefit are not applicable for energy efficiency scheduling issue due to the neglecting of recycle and lost energy,as well as critical operation parameters as coil outlet pressure(COP)and dilution ratio.In addition,the scheduling solutions mostly regard each cracking furnace as an elementary unit,regardless of the coordinated operation of internal dual radiation chambers(DRC).Therefore,to improve energy utilization and production operation,a novel energy efficiency scheduling solution for ethylene cracking process is proposed in this paper.Specifically,steam heat recycle and exhaust heat loss are considered in cracking process based on 6 types of extreme learning machine(ELM)based cracking models incorporating DRC operation and three operation parameters as coil outlet temperature(COT),COP,and dilution ratio according to semi-mechanism analysis.Then to provide long-term decision-making basis for energy efficiency scheduling,overall energy efficiency indexes,including overall output per unit net energy input(OONE),output-input ratio per unit net energy input(ORNE),exhaust gas heat loss ratio(EGHL),are designed based on input-output analysis in terms of material and energy flows.Finally,a multiobjective evolutionary algorithm based on decomposition(MOEA/D)is employed to solve the formulated multi-objective mixed-integer nonlinear programming(MOMINLP)model.The validities of the proposed scheduling solution are illustrated through a case study.The scheduling results demonstrate that an optimal balance between multi-flow allocation,multi-parameter setting,and DRC coordinated operation is reached,which achieves 3.37%and 2.63%decreases in net energy input for same product output and conversion ratio,as well as the 1.56%decrease in energy loss ratio.

TENSOR SUM AND DYNAMICAL SYSTEMS

In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.

A description of Kac-systems of multiplicative unitary operators

Let V be a multiplicative unitary operator on a separable Hilbert spaceH, then there are two subalgebras ofB( H) denoted byA( V) and ?( V), respectively, which correspond to V. If V satisfiesV 2 =I, then we will obtain the necessary and sufficient condition of Baaj and Skandalis’ main theorem, i.e.V has a Kac-system if and only if the linear closed space of the product of the above two algebras is the compact operator space; with this condition the above algebras are also quantum groups.

Existence results for degenerate p(x)-Laplace equations with Leray-Lions type operators

We show the existence and multiplicity of solutions to degenerate p(x)-Laplace equations with Leray-Lions type operators using direct methods and critical point theories in Calculus of Variations and prove the uniqueness and nonnegativeness of solutions when the principal operator is monotone and the nonlinearity is nonincreasing. Our operator is of the most general form containing all previous ones and we also weaken assumptions on the operator and the nonlinearity to get the above results. Moreover, we do not impose the restricted condition on p(x) and the uniform monotonicity of the operator to show the existence of three distinct solutions.

Reducing subspaces of tensor products of weighted shifts

A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and only if A and B are unitarily equivalent.We also study the reducing subspaces of A^kI+IB^l and give some examples.As an application,we study the reducing subspaces of multiplication operators Mzk+αωl on function spaces.

Invariant Subspaces of Sobolev Disk Algebra

In this paper, we study the invariant subspaces of the operator Mz on the Sobolev disk algebra R（D） and characterize the invariant subspace with finite codimension.