A Simple Proof for a Property of the Vector Space Ⅴ Over the Field F

<正> In this paper we'll prove a fundameutal property of the vector space by means of the ex-tension field,i.e.the numbers of the elements of a basis of the vector space V over the field Fequal to the d imensions(V:F).     

Spectrum of Normal Weighted Composition Operators on the Fock Space Over ℂN

By using commutative C^*-algebra techniques, spectrum and essential spectrum of normal weighted composition operators on the Fock space over C^N are completely characterized. As an application, spectrum of self-adjoint weighted composition operators on the Fock space are obtained also.     

Asymptotic Expansion of M ‐Estimator Over Wiener Space

In this paper we consider an Mestimator defined as a solution of a given estimating function. Sufficient conditions of existence of an Mestimator and its stochastic expansion are presented. In the case where the underlying probability space is a Wiener space and the leading term of the stochastic expansion is a martingale, asymptotic expansions of its distribution function are obtained with the aid of Malliavin calculus. Applications to a stationary ergodic diffusion model are also discussed.     

Some Properties of Bounded Linear Operator Over L_p Space

<正> We shall extend the concepts of the kernel and the image of the homomorphism φ in Abstract Algebra to the bounded linear operator of L_p space. We can obtain some results. Definition 1 let A be a L_p space, B(?)A. If B is a L_p space by the operation and the norm in A, then the subset B of A is called a L_p subspace of A.     

On the Smallest Base of the Stone Space

51.IntroductionandDefinitionIn[l]ithadbeenprovedthat:ifadistributivelatticeLpossessesthesmal1estsetofgen-eratingelements,thenLsatisfiesjointinfinitelydistributivelaw.AndinL2jproved:acom-pletelydistributivelatticepossessesminimalsetofgeneratingelements,thenLisastrongalge-bra.lnthispaper,theconceptofthesetofgeneraingelementsisdifferentfrom[1j.Wewillsolvetheexistenceproblemoftheminimalsetofgeneratingelementsbyuseofthetopologicalrepresentation.Firstwedefinethesmallestbase,strongopensetinthetopol…     

The Fine Spectra of the Difference Operator △ Over the Sequence Space bvp, （1 ≤ p 〈 ∞）^＊

The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.     

Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space

Let ${{\varphi}}$ be an analytic self-map of the open unit disk ${{\mathbb{D}}}$ in the complex plane ${{\mathbb{C}, H(\mathbb{D})}}$ the space of complex-valued analytic functions on ${{\mathbb{D}}}$ , and let u be a fixed function in ${{H(\mathbb{D})}}$ . The weighted composition operator is defined by $$(uC_{\varphi}f)(z) = u(z)f({\varphi}(z)), \quad z \in \mathbb{D}, f \in H(\mathbb{D}).$$ In this paper, we study the boundedness and the compactness of the weighted composition operators from the minimal Möbius invariant space into the Bloch space and the little Bloch space.     

Besov Functions and Tangent Space to the Integrable Teichmüller Space

The authors identify the function space which is the tangent space to the integrable Teichm¨uller space. By means of quasiconformal deformation and an operator induced by a Zygmund function, several characterizations of this function space are obtained.     

On the Quaternion Ball and the Quaternion Projective Space

Since the quaternion ball was used to study the AdS/CFT problems tor spinor fields, it is worthwhile to study further the geometry （in sense of Klein） and analysis on it and on its extended space （in the sense of Behnke-Thullen）, the quaternion projective space.     

μ-Average n-Widths on the Wiener Space

In this paper we consider the μ-average widths of integral operator T^m on the Wiener space C. Some weakly asymptotically exact estimates for the Gelfand width and other widths are obtained.     

The Moduli Space of Points in the Boundary of Complex Hyperbolic Space

We consider the space M(n,m)\mathcal{M}(n,m) of ordered m-tuples of distinct points in the boundary of complex hyperbolic n-space, H_\mathbbCⁿ\mathbf{H}_{\mathbb{C}}^{n}, up to its holomorphic isometry group PU(n,1). An important problem in complex hyperbolic geometry is to construct and describe the moduli space for M(n,m)\mathcal{M}(n,m). In particular, this is motivated by the study of the deformation space of complex hyperbolic groups generated by loxodromic elements. In the present paper, we give the complete solution to this problem.     

On the Constructions of the Non-Abelian p 3-Extensions Over ℚ

Let p be an odd prime, and let G be one of the two non-abelian groups of order p ³. Ledet [3 Ledet , A. ( 2000 ). Generic and explicit realization of small p-groups . Journal of Symbolic Computation 30 : 859 – 865 . [Google Scholar]] described explicit G-extensions over the rationales in special cases. In this article, we generalize his results and show how non-tame G-extensions can be constructed having exactly two ramified primes.     

On the Number of Vedernikov–Ein Irreducible Components of the Moduli Space of Stable Rank 2 Bundles on the Projective Space

We propose a method for finding the exact number of Vedernikov–Ein irreducible components of the first and second types in the moduli space M(0, n) of stable rank 2 bundles on the projective space P³ with Chern classes c₁ = 0 and c₂ = n ≥ 1. We give formulas for the number of Vedernikov–Ein components and find a criterion for their existence for arbitrary n ≥ 1.     

Bounded Hankel Products on the Weighted Bergman Space

1 Introduetion The Bergman spaeeA足15 the spaee of analytie funetions on a plane domain D whieh are square integrable with resPeet to the measure dA。(:)=(a 1)(1一l:I“)“己且(之)，where dA denotes the normalized Lebesgue area measure on D.The reProdueing kernel in A蕊15 given妙K1a)(:) 1 (1一场:)2 a之，叨任D. If(·，·)。denotes the inner produet in LZ(D，dA。)，then (。，K;a))。=人(二) h oA蕊，二。D. The orthogonal projeetion凡of LZ(D，dA。)ontoA且15 given by‘Pa。)(?卜(。，玲，)一…     

k-order Slant Toeplitz Operators on the Bergman Space

In this paper κ-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed.     

Some Notes About the Cardinals of Metric Space

Theorem 1 Let X be a nonempty countable set, K={: is a discrete metric space}, define ≌ iff((?)f) (f is an equilong isomorphism from to , for a given ∈K, define = { ∈K: ≌}. Let C={: ∈K},then |C|=|K|=|{d:d is a metric on X}|=2~((?)0) The Theorem 2 illustrates that there exists a nonempty countable set X on which we can define 2~((?)0) nondiscrete metric spaces such that they are not isomorphic each other.     

Compactness of Product Operators on the Bergman Space

In this paper, we study the compactness of the product of a composition operator with another one＇s adjoint on the Bergman space. Some necessary and sufficient conditions for such operators to be compact are given.     

The Compact Characterhations of the Operator H_fH_g on the Bergman Space

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