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1.
We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set.  相似文献   

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丘京辉 《数学学报》2006,49(6):1231-123
本文研究Retakh's条件(M_0),正则性和弱序列式回缩性之间的关系.对于(LM)-空间,弱序列式回缩性等价于正则性加上一个介于(Q_0)和(M_0)之间的条件对于(LN)-空间,我们获得了更满意的结果,证明了弱序列式回缩性等价于正则性加上条件(M_0),也等价于一个非常弱的正则性条件加上条件(M_0)(见文献[1-28]).  相似文献   

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We investigate the existence of a separately continuous function f: X × Y → ℝ with a one-point set of discontinuity points in the case where the topological spaces X and Y satisfy conditions of compactness type. In particular, it is shown that, for compact spaces X and Y and nonisolated points x 0X and y 0Y, a separately continuous function f: X × Y → ℝ with the set of discontinuity points {(x 0, y 0)} exists if and only if there exist sequences of nonempty functionally open sets in X and Y that converge to x 0 and y 0, respectively.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 94–101, January, 2005.  相似文献   

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Any analytic map φ of the unit disc ${\mathbb{D}}$ into itself induces a composition operator C φ on BMOA, mapping ${f \mapsto f \circ \varphi}$ , where BMOA is the Banach space of analytic functions ${f\colon \mathbb{D} \to \mathbb{C}}$ whose boundary values have bounded mean oscillation on the unit circle. We show that C φ is weakly compact on BMOA precisely when it is compact on BMOA, thus solving a question initially posed by Tjani and by Bourdon, Cima and Matheson in the special case of VMOA. As a crucial step of our argument we simplify the compactness criterion due to Smith for C φ on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. Additional equivalent compactness criteria are established. Furthermore, we prove the unexpected result that compactness of C φ on VMOA implies compactness even from the Bloch space into VMOA.  相似文献   

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Retakh条件(M0)与弱(序列式)紧正则性   总被引:1,自引:0,他引:1  
本文研究了弱(序列式)紧正则诱导极限与凸弱(序列式)紧正则诱导极限.满足Retakh条件(Mo)的(LF)-空间必为凸弱(序列式)紧正则的,但未必为弱(序列式)紧正则的.对于弱序列式完备Frechet空间的可数诱导极限,Retakh条件(Mo)蕴涵弱(序列式)紧正则性.特别地,对于Kothe(LF)-序列空间Ep(1≤p<∞),Retakh条件(Mo)等价于弱(序列式)紧正则性.对于这类空间,利用Vogt的有关结论,给出了弱(序列式)紧正则性的特征.  相似文献   

7.
本文研究了弱(序列式)紧正则诱导极限与凸弱(序列式)紧正则诱导极限.满足Retakh条件(M0)的(LF)-空间必为凸弱(序列式)紧正则的,但未必为弱(序列式)紧正则的.对于弱序列式完备Frechet空间的可数诱导极限,Retakh条件(M0)蕴涵弱(序列式)紧正则性.特别地,对于Kothe(LF)-序列空间Ep(1≤p<∞),Retakh条件(M0)等价于弱(序列式)紧正则性.对于这类空间,利用Vogt的有关结论,给出了弱(序列式)紧正则性的特征.  相似文献   

8.
This paper shows that, contrary to the case of linear operators, absolutely summing homogeneous polynomials are not always weakly compact. It is also shown that, regardless of the infinite dimensional Banach space E and the positive integer n, there exists an n-homogeneous polynomial P from E to E that plays the role of the identity operator in the sense that P is neither compact nor absolutely r-summing for any r, and P is weakly compact if and only if E is reflexive.  相似文献   

9.
The authors study the algebra of uniformly continuous holomorphicsymmetric functions on the ball of lp, investigating in particularthe spectrum of such algebras. To do so, they examine the algebraof symmetric polynomials on lp-spaces, as well as finitely generatedsymmetric algebras of holomorphic functions. Such symmetricpolynomials determine the points in lp up to a permutation.  相似文献   

10.
We investigate necessary and sufficient conditions on topological products X = ∏s ∈ s X s and Y = ∏t ∈ T Y t for every separately continuous function f: X × Y → ℝ to be dependent on at most ℵ coordinates with respect to a certain coordinate.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1357 – 1368, October, 2004.  相似文献   

11.
本用度量空间的mssc-映象给出了N-空间一些刻画,证明了空间X是N-空间当且仅当X是度量空间的序列覆盖(序列商)mssc-映象,肯定地回答了关于N-空间的一个猜想.  相似文献   

12.
Let P be an elliptic differential operator of order p with real analytic coefficients on in open set Q ? ?n. Given a compact set K ? Ω, we describe the closure in BMO(K) of the space of mentions of Pf = 0 on neighborhoods of K.  相似文献   

13.
For weakly closed surjections between arbitrary topological spaces conditions are sought which assure a HAUSDORFF range. Some results of T. NOIRI are corrected and/or improved, and some results of J. K. KOHLI are slightly strengthened.  相似文献   

14.
For every bounded linear operator T in L1[0, 1] there is an element of best approximation in the ideal of weakly compact operators. We also give some sufficient conditions for ‖T+S‖ = ‖T‖ + ‖S‖, where S and T are L1-operators.  相似文献   

15.
丘京辉  QIU Jing-hui 《数学学报》2000,43(6):1105-111
本文研究了(LM)-空间(即:可尺度局部凸空间序列的诱导极限)中,Re-takh’s条件(M)与序列式回缩性之间的关系,给出了满足Retakh’s条件(M)的(LM)-空间为序列式回缩的一系列特征条件.  相似文献   

16.
We introduce a new parametric representation of the class of holomorphic functions in the unit disk such that their Nevanlinna characteristic has a power growth near the boundary of the disk. The parameters of the obtained representation are determined explicitly by values of the function. In addition, the set of multipliers from the considered class to the Hardy and Bergman classes and the disk algebra is described completely. Bibliography: 10 titles.  相似文献   

17.
Algebras Generated by Holomorphic and Harmonic Functions on the Disc   总被引:1,自引:0,他引:1  
Let E be a subset of the boundary of the open unit disc D, andlet A be the algebra of bounded holomorphic functions on D thatextend continuously to D E. It is shown that if f is a boundedharmonic function on D that extends continuously to D E andis not holomorphic, then the uniformly closed algebra A[f] generatedby A and f contains . This result contains as special cases a result on the disc algebradue to irka and a result on H(D due to Axler and Shields. Astronger form of the result, in which f is allowed to have discontinuitieson a small subset of E, is also established. 2000 MathematicsSubject Classification 46J10, 46J15, 30H05.  相似文献   

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