Abstract
This paper presents a survey of the contributions of mathematicians in Harbin to some topics of Banach spaces and topological vector spaces, especially, to Köthe sequence spaces and the infinite matrix operator algebras on them, Banach spaces containing no copy of C 0, abstract functions and integrals, differentiability of convex functions and abstract duality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wu Congxin, Perfect spaces and perfect matrix rings (I), Science Record, 3(1959), 95–102.
---, Perfect spaces and perfect matrix rings (II), Science Record, 3(1959), 103–106.
---, Perfect spaces and perfect matrix rings (III), Acta Math. Sinica, 14(1964), 319–327.
---, On the complete continuity of matrix operators in perfect spaces, J. Jilin Univ., (1962), no. 1, 61–66.
---, Ideals of completely continuous matrix operators in perfect spaces, J. Harbin Inst. of Tech. (1977), no. 3, 32–38.
---, Perfect matrix algebras (I), Acta Math. Sinica, 21(1978), 161–170.
---, Some problems of nuclear perfect spaces, Acta Math. Sinica, 22(1979), 653–666.
---, Characterizations for normedness and metrizability of sequence spaces, J. Harbin Inst, of Tech., (1993), no. 4.
Wu Congxin, Wang Hongtao, Matrix algebra Σ(λ, μ) and its topologies, J. Harbin Inst, of Tech., Math, issue (1984), 1–5.
---, ---, Multiplicative continuity under strong topology for Σ(λ, μ), Science Bulletin, 30(1985), 157–158.
---, ---, Multiplicative continuity under strong topology for Σ(λ, μ) on convergence free spaces, J. Harbin Inst, of Tech., Math, issue (1985), 12–15.
Wu Congxin, Liu Lei, Matrix transformations on some vectorvalued sequence spaces, SEA Bull. Math., 17(1993), no. 1.
Liu Lei, Wu Congxin, The topology on sequence spaces with values in Banach spaces, J. Harbin Inst, of Tech., Math, issue (1991), 8–9.
Wu Congxin, Bu Qingying, The vector-valued sequence space l p[X] and Banach spaces not containing a copy of C 0, A Friendly Collection of Mathematical Papers I, Jilin Univ. Press, (1990), 9–16.
---, ---, Vector-valued sequence space Λ[X] and its Köthe dual (I), J. Northeastern Math., 8(1992), 275–282.
Wu Congxin, Bu Qingying, Characterizations of CMC (X) being GAK-space, J. Harbin Inst, of Tech., (1993), no. 1, 93–96.
---, ---, Köthe dual of Banach sequence spaces l p [X] and Grothendieck space, Comment. Math. Univ. Caroline, 34(1993), no. 2.
---, ---, The sequential completeness of operator spaces L(l p , X) and K(l p , X), J. Math. Res. & Expos., 12(1992), 366.
---, ---, Unconditionally convergent series of operators on Banach spaces, J. Math. Anal. Appl., to appear.
---, ---, Banach sequence spaces l p [X] and their properties, SEA Bull. Math., to appear.
---, ---, Locally convex spaces containing no copy of Co, J. Math. Anal. Appl, 172(1993), 205–211.
Bu Qingying, The locally convex space X for which λ(X) =λ[X], J. Harbin Inst, of Tech., Math, issue (1991), 142–144.
---, Barrelledness of vector-valued sequence space C 0 (X), J. Congcheng Shuxue Xuebao, 9(1992), 64–72.
---, Sequential representation of compact operator space K(l p , X), Hebei Jidian Xueyuan Xuebao, 10(1993), no. 2, 62–68.
---, Barrelledness of vector-valued sequence space Λ(X), J. Harbin Inst, of Tech, (1993), no. 4.
---, Ideal of infinite matrix operators on perfect sequence spaces, Functiones of Approximation, 22(1993).
Jiang Zejian and Zou Chengzu, On spectral operators, J. of Jilin Univ., 1(1964), 65–74.
Li Ronglu, A characterization of Banach spaces containing no copy of c0, Bull. Chin. Sci, 7(1984), 444.
Wu Congxin and Xue Xiaoping, Bounded linear operators from Banach spaces not containing c0 into l1, J. of Math. (PRC), vol. 12, 4(1992), 430–434.
Wu Congxin and Liu Tiefu, Abstract bounded second variation functions, Northeastern Math. J, 1(1985) 41–53.
Wu Congxin and Liu Tiefu, Abstract kth bounded variation functions, Science Bulletin, 31(1986), 931–932.
Wu Congxin and Xue Xiaoping, Abstract bounded variation functions on locally convex space, Acta Math. Sinica, 33(1990), 107–112.
Wu Congxin, Abstract bounded variation functions on sequence space (I), J. Harbin Inst, of Tech, (1959), no.2, 93–100.
Wu Congxin, Abstract bounded variation functions on sequence space (II), Acta Math. Sinica, 13(1963), 548–557.
Wu Congxin, Abstract bounded variation functions on sequence space, Scientia Sinica, 13(1964), 1359–1380.
Wu Congxin and Zao Linsheng, Abstract 2nd bounded variation functions on sequence space (I), J. Math. Res. Exp, 2(1982), no. 4, 143–150.
Wu Congxin and Zao Linsheng, Abstract 2nd bounded variation functions on sequence space (I), J. Math. Res. Exp, 4(1982), no. 1, 97–106.
Wu Congxin and Liu Tiefu, Some notes of the abstract functions of 2nd absolute continuity, Science Bulletin, 31(1986), 646–647, Northeastern Math. J., 2(1986), 371–378.
Wu Congxin and Liu Tiefu, Abstract functions of absolute kth continuity, J. Harbin Inst, of Tech., (1986) no. 1, 123–124.
Wu Congxin and Xue Xiaoping, Abstract functions of absolute continuity on locally convex space, Chin. Annals of Math., 12A(1990), Supplement, 84–86.
Wu Congxin and Zao Linsheng and Liu Tiefu, Bounded variation functions and their generalizations and applications, Heilongjiang Scientific & Technique Pub. House, 1988.
Wu Congxin and Xue Xiaoping, A remark of Pettis integral, Science Bulletin, 34(1989), 1836.
Wu Congxin and Zhang Bo, Riemann-Stieltjes integral on abstract functions, J. Harbin Inst, of Tech., (1990) no. 2, 1–7.
Liu Tiefu, Linear oprator between D[a, b] and a Banach space E, J. Math., 1(1988) no. 2, 105–112.
Wu Congxin and Ma Ming, Bounded variation of abstract function whose value is in a Banach lattice, Northeastern Math. J., 8(1992), 293–298.
Xue Xiaoping and Zhang Bo, Properties of set-valued function with bounded variation in Banach space, J. Harbin Inst, of Tech., (1991) no. 3, 102–105.
Wu Congxin and Cheng Lixin, A note on the differentiability of convex functions, Proc. Amer, Math. Soc. 121(1994), 1057–1062.
Wu Congxin and Cheng Lixin, Characterizations of the differentiability points of the norms on co(Γ) and l∞(Γ), Northeastern Math. J. (to appear).
Cheng Lixin and Wei Wenzhan, A Generalized Hahn-Banach extension theorm, J. Guanxi Teacher’s College, No. 4(1988).
Cheng Lixin and Chen Lianchang, The final answer for an open problem, J. Jianghan Petro. Inst. (3) 10(1988), 136–138.
Chen Shoutao, Sun Huiying and Wu Congxin, λ-Property of Orlicz spaces, Bull. Polish Acad. Sci. Math. 39(1991), 63–69.
Cheng Lixin, Orthogonalities of Banach spaces, J. Jianghan Petrol. Inst. (1) 9(1987), 1–5.
S. Kaijser and Q. Guo, An estimate of the Minkowski distance between convex bodies. Uppsala Univ. Dept. Math Report 1(1992).
J. Zhu, Topics in Banach space theory. Doctorial thesis of Lancaster Univ, Britain.
Chen Shoutao and Wang Yuwein. On definition of non-squane normed spaces, Chin. Ann. of Math. 9A(1988), 330–334.
Wu Congxin and Sun Huiying, On complex uniform convexity of Musielak-Orlicz spaces. Northeastern Math. J. 4(1988), 389–396.
Wu Congxin and Guo Qi, On uniform convexity of locally convex spaces, Chin. Ann. of Math. 11A(1990), 351–354.
Guo Qi and Wu Congxin, Strict convexity and smoothness in locally convex spaces, Northeastern Math. J., 5(1989), 465–472.
Wu Congxin and Guo Qi, Uniform convexity and strict convexity in metric linear space, J. Liaoning Univ., (1989) No.3, 1–5.
Wu Congxin and Li Yongjing; Extreme points and linear bounded operators, Northeastern Math. J, 8(1992), 475–476.
Li Yongjin, Almost uniform convexity and reflexivity, J. Harbin Inst, of Tech, 9(1991) Supplement, 145–147.
Li Yongjin, Complex convexity and complex smoothness, J. of Math, 12(1992).
Li Yongjin, A note of WLUC points, J. Univ., (1992) No. 1.
Cheng Lixin, Chen Lianchang and Cheng Wei. Orthogonalities of Banach spaces and Hilbert space. J. Daqing Petro. Inst. (4) 13(1989), 75–77.
Cheng Lixin and Chen Lianchang, Comment:“L p-orthogonality of Banach space”, J. Math. Res. Exp. (1) 7(1987), 175–176.
Cheng Lixin, Wang Tinfu and Chen Lianchang, A new class of characteristic functions for Banach spaces. J. Nature (8) (1988), 633–634; J. Harbin Univ. of Sci and Tech, (3) (1988), 93–97.
Chen Lixin, Subinner-product and suborthogonality in Banach spaces, J. Jianghan Petrol. Inst. (1) 12(1990), 80–89.
Cheng Lixin, On the characteristic functions of Banach spaces, J. Jianghan Petro. Inst. (3) 15(1993).
Cheng Lixin, Cheng Lianchang and Wei Weinzhan, The claracteristic functions and the moduli of convexity and smoothness of Banach spaces, J. of Math, 10(1990), 309–314.
S. Kaijser and Q. Guo, A Dvoretzky theorem for general convex bodies, Uppsala Univ. Dept. of Math. Report 1(1992).
Wu Congxin and Cheng Lixin, Extensions of the Preiss Differentiability, Theorem, J. Funct. Anal. 124(1994), 112–118.
Cheng Lixin and Nan Chaoxun, A sufficiency and necessity condition for Gateaux and Frechet differentiability of continuous gauges on Banach spaces, Bull. Sci, 34(1989), 795.
Cheng Lixin, Li Jianhua and Nan Chaoxun, Gateaux and Frechet differentiability of continuous gauges on Banach spaces, Adv. in Math, 20(1991), 326–333.
Cheng Lixin, Two notes on the smoothensss of Banch spaces, J. Math. Res. Exp. 9(1989), 315–316.
Cheng Lixin, Smoothness and strong smoothness of Banach spaces, J. Jianghan Petro. Inst. (1) 11(1989), 102–107.
Cheng Lixin and Wei Wenzhan, Some differentiability properties of continuous convex Functions on Banach spaces, J. Guanxi Univ. (1) 16(1991), 65–70.
Cheng Lixin, Differentiability of convex functions and Asplund spaces, Acta. Math. Sci. (1) 15(1995).
Wu Congxin and Cheng Lixin, On weak Asplund spaces, to appear.
Wu Congxin and Cheng Lixin, Differentiability of convex functions on locally convex spaces, J. Harbin Inst, of Tech., E-l, 1(1994), 7–12.
---, ---, Approximation of functions on metric spaces and its application to differentiability of convex functions on meager sets, Wuhan Univ. Press, 1995.
Li Ronglu and C. Swartz, K-convergence and the Orlicz-Pettis theorem, publ. De’Inst. Math, Tome 49(63), 1991, 117–122.
---, ---, Spaces for which the uniform convergence principle holds, Studia Sci. Math. Hungarica, 27(1992), 373–384.
---, ---, A nonlinear Schur theorem, Acta Sci. Math, to appear.
---, --- and Cho Min-Hyung, Abstract duality, to appear.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Wu, C. (1996). Research on Some Topics of Banach Spaces and Topological Vector Spaces in Harbin. In: Li, B., Wang, S., Yan, S., Yang, CC. (eds) Functional Analysis in China. Mathematics and Its Applications, vol 356. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0185-8_17
Download citation
DOI: https://doi.org/10.1007/978-94-009-0185-8_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6567-2
Online ISBN: 978-94-009-0185-8
eBook Packages: Springer Book Archive