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Research on Some Topics of Banach Spaces and Topological Vector Spaces in Harbin

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Functional Analysis in China

Part of the book series: Mathematics and Its Applications ((MAIA,volume 356))

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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.

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References

  1. Wu Congxin, Perfect spaces and perfect matrix rings (I), Science Record, 3(1959), 95–102.

    Google Scholar 

  2. ---, Perfect spaces and perfect matrix rings (II), Science Record, 3(1959), 103–106.

    Google Scholar 

  3. ---, Perfect spaces and perfect matrix rings (III), Acta Math. Sinica, 14(1964), 319–327.

    MathSciNet  MATH  Google Scholar 

  4. ---, On the complete continuity of matrix operators in perfect spaces, J. Jilin Univ., (1962), no. 1, 61–66.

    Google Scholar 

  5. ---, Ideals of completely continuous matrix operators in perfect spaces, J. Harbin Inst. of Tech. (1977), no. 3, 32–38.

    Google Scholar 

  6. ---, Perfect matrix algebras (I), Acta Math. Sinica, 21(1978), 161–170.

    MathSciNet  Google Scholar 

  7. ---, Some problems of nuclear perfect spaces, Acta Math. Sinica, 22(1979), 653–666.

    MathSciNet  Google Scholar 

  8. ---, Characterizations for normedness and metrizability of sequence spaces, J. Harbin Inst, of Tech., (1993), no. 4.

    Google Scholar 

  9. Wu Congxin, Wang Hongtao, Matrix algebra Σ(λ, μ) and its topologies, J. Harbin Inst, of Tech., Math, issue (1984), 1–5.

    Google Scholar 

  10. ---, ---, Multiplicative continuity under strong topology for Σ(λ, μ), Science Bulletin, 30(1985), 157–158.

    Google Scholar 

  11. ---, ---, Multiplicative continuity under strong topology for Σ(λ, μ) on convergence free spaces, J. Harbin Inst, of Tech., Math, issue (1985), 12–15.

    Google Scholar 

  12. Wu Congxin, Liu Lei, Matrix transformations on some vectorvalued sequence spaces, SEA Bull. Math., 17(1993), no. 1.

    Google Scholar 

  13. Liu Lei, Wu Congxin, The topology on sequence spaces with values in Banach spaces, J. Harbin Inst, of Tech., Math, issue (1991), 8–9.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. ---, ---, Vector-valued sequence space Λ[X] and its Köthe dual (I), J. Northeastern Math., 8(1992), 275–282.

    MATH  Google Scholar 

  16. Wu Congxin, Bu Qingying, Characterizations of CMC (X) being GAK-space, J. Harbin Inst, of Tech., (1993), no. 1, 93–96.

    Google Scholar 

  17. ---, ---, Köthe dual of Banach sequence spaces l p [X] and Grothendieck space, Comment. Math. Univ. Caroline, 34(1993), no. 2.

    Google Scholar 

  18. ---, ---, The sequential completeness of operator spaces L(l p , X) and K(l p , X), J. Math. Res. & Expos., 12(1992), 366.

    Google Scholar 

  19. ---, ---, Unconditionally convergent series of operators on Banach spaces, J. Math. Anal. Appl., to appear.

    Google Scholar 

  20. ---, ---, Banach sequence spaces l p [X] and their properties, SEA Bull. Math., to appear.

    Google Scholar 

  21. ---, ---, Locally convex spaces containing no copy of Co, J. Math. Anal. Appl, 172(1993), 205–211.

    Article  MathSciNet  MATH  Google Scholar 

  22. Bu Qingying, The locally convex space X for which λ(X) =λ[X], J. Harbin Inst, of Tech., Math, issue (1991), 142–144.

    Google Scholar 

  23. ---, Barrelledness of vector-valued sequence space C 0 (X), J. Congcheng Shuxue Xuebao, 9(1992), 64–72.

    Google Scholar 

  24. ---, Sequential representation of compact operator space K(l p , X), Hebei Jidian Xueyuan Xuebao, 10(1993), no. 2, 62–68.

    Google Scholar 

  25. ---, Barrelledness of vector-valued sequence space Λ(X), J. Harbin Inst, of Tech, (1993), no. 4.

    Google Scholar 

  26. ---, Ideal of infinite matrix operators on perfect sequence spaces, Functiones of Approximation, 22(1993).

    Google Scholar 

  27. Jiang Zejian and Zou Chengzu, On spectral operators, J. of Jilin Univ., 1(1964), 65–74.

    Google Scholar 

  28. Li Ronglu, A characterization of Banach spaces containing no copy of c0, Bull. Chin. Sci, 7(1984), 444.

    Google Scholar 

  29. 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.

    MATH  Google Scholar 

  30. Wu Congxin and Liu Tiefu, Abstract bounded second variation functions, Northeastern Math. J, 1(1985) 41–53.

    MATH  Google Scholar 

  31. Wu Congxin and Liu Tiefu, Abstract kth bounded variation functions, Science Bulletin, 31(1986), 931–932.

    Google Scholar 

  32. Wu Congxin and Xue Xiaoping, Abstract bounded variation functions on locally convex space, Acta Math. Sinica, 33(1990), 107–112.

    MathSciNet  MATH  Google Scholar 

  33. Wu Congxin, Abstract bounded variation functions on sequence space (I), J. Harbin Inst, of Tech, (1959), no.2, 93–100.

    Google Scholar 

  34. Wu Congxin, Abstract bounded variation functions on sequence space (II), Acta Math. Sinica, 13(1963), 548–557.

    Google Scholar 

  35. Wu Congxin, Abstract bounded variation functions on sequence space, Scientia Sinica, 13(1964), 1359–1380.

    MathSciNet  Google Scholar 

  36. Wu Congxin and Zao Linsheng, Abstract 2nd bounded variation functions on sequence space (I), J. Math. Res. Exp, 2(1982), no. 4, 143–150.

    Google Scholar 

  37. Wu Congxin and Zao Linsheng, Abstract 2nd bounded variation functions on sequence space (I), J. Math. Res. Exp, 4(1982), no. 1, 97–106.

    Google Scholar 

  38. 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.

    Google Scholar 

  39. Wu Congxin and Liu Tiefu, Abstract functions of absolute kth continuity, J. Harbin Inst, of Tech., (1986) no. 1, 123–124.

    Google Scholar 

  40. Wu Congxin and Xue Xiaoping, Abstract functions of absolute continuity on locally convex space, Chin. Annals of Math., 12A(1990), Supplement, 84–86.

    Google Scholar 

  41. Wu Congxin and Zao Linsheng and Liu Tiefu, Bounded variation functions and their generalizations and applications, Heilongjiang Scientific & Technique Pub. House, 1988.

    Google Scholar 

  42. Wu Congxin and Xue Xiaoping, A remark of Pettis integral, Science Bulletin, 34(1989), 1836.

    Google Scholar 

  43. Wu Congxin and Zhang Bo, Riemann-Stieltjes integral on abstract functions, J. Harbin Inst, of Tech., (1990) no. 2, 1–7.

    Google Scholar 

  44. Liu Tiefu, Linear oprator between D[a, b] and a Banach space E, J. Math., 1(1988) no. 2, 105–112.

    Google Scholar 

  45. Wu Congxin and Ma Ming, Bounded variation of abstract function whose value is in a Banach lattice, Northeastern Math. J., 8(1992), 293–298.

    MATH  Google Scholar 

  46. 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.

    Google Scholar 

  47. Wu Congxin and Cheng Lixin, A note on the differentiability of convex functions, Proc. Amer, Math. Soc. 121(1994), 1057–1062.

    Article  MathSciNet  MATH  Google Scholar 

  48. Wu Congxin and Cheng Lixin, Characterizations of the differentiability points of the norms on co(Γ) and l∞(Γ), Northeastern Math. J. (to appear).

    Google Scholar 

  49. Cheng Lixin and Wei Wenzhan, A Generalized Hahn-Banach extension theorm, J. Guanxi Teacher’s College, No. 4(1988).

    Google Scholar 

  50. Cheng Lixin and Chen Lianchang, The final answer for an open problem, J. Jianghan Petro. Inst. (3) 10(1988), 136–138.

    Google Scholar 

  51. Chen Shoutao, Sun Huiying and Wu Congxin, λ-Property of Orlicz spaces, Bull. Polish Acad. Sci. Math. 39(1991), 63–69.

    MathSciNet  Google Scholar 

  52. Cheng Lixin, Orthogonalities of Banach spaces, J. Jianghan Petrol. Inst. (1) 9(1987), 1–5.

    Google Scholar 

  53. S. Kaijser and Q. Guo, An estimate of the Minkowski distance between convex bodies. Uppsala Univ. Dept. Math Report 1(1992).

    Google Scholar 

  54. J. Zhu, Topics in Banach space theory. Doctorial thesis of Lancaster Univ, Britain.

    Google Scholar 

  55. Chen Shoutao and Wang Yuwein. On definition of non-squane normed spaces, Chin. Ann. of Math. 9A(1988), 330–334.

    Google Scholar 

  56. Wu Congxin and Sun Huiying, On complex uniform convexity of Musielak-Orlicz spaces. Northeastern Math. J. 4(1988), 389–396.

    MATH  Google Scholar 

  57. Wu Congxin and Guo Qi, On uniform convexity of locally convex spaces, Chin. Ann. of Math. 11A(1990), 351–354.

    Google Scholar 

  58. Guo Qi and Wu Congxin, Strict convexity and smoothness in locally convex spaces, Northeastern Math. J., 5(1989), 465–472.

    MATH  Google Scholar 

  59. Wu Congxin and Guo Qi, Uniform convexity and strict convexity in metric linear space, J. Liaoning Univ., (1989) No.3, 1–5.

    Google Scholar 

  60. Wu Congxin and Li Yongjing; Extreme points and linear bounded operators, Northeastern Math. J, 8(1992), 475–476.

    MATH  Google Scholar 

  61. Li Yongjin, Almost uniform convexity and reflexivity, J. Harbin Inst, of Tech, 9(1991) Supplement, 145–147.

    Google Scholar 

  62. Li Yongjin, Complex convexity and complex smoothness, J. of Math, 12(1992).

    Google Scholar 

  63. Li Yongjin, A note of WLUC points, J. Univ., (1992) No. 1.

    Google Scholar 

  64. Cheng Lixin, Chen Lianchang and Cheng Wei. Orthogonalities of Banach spaces and Hilbert space. J. Daqing Petro. Inst. (4) 13(1989), 75–77.

    Google Scholar 

  65. Cheng Lixin and Chen Lianchang, Comment:“L p-orthogonality of Banach space”, J. Math. Res. Exp. (1) 7(1987), 175–176.

    Google Scholar 

  66. 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.

    Google Scholar 

  67. Chen Lixin, Subinner-product and suborthogonality in Banach spaces, J. Jianghan Petrol. Inst. (1) 12(1990), 80–89.

    Google Scholar 

  68. Cheng Lixin, On the characteristic functions of Banach spaces, J. Jianghan Petro. Inst. (3) 15(1993).

    Google Scholar 

  69. 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.

    MATH  Google Scholar 

  70. S. Kaijser and Q. Guo, A Dvoretzky theorem for general convex bodies, Uppsala Univ. Dept. of Math. Report 1(1992).

    Google Scholar 

  71. Wu Congxin and Cheng Lixin, Extensions of the Preiss Differentiability, Theorem, J. Funct. Anal. 124(1994), 112–118.

    Article  MathSciNet  MATH  Google Scholar 

  72. 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.

    Google Scholar 

  73. Cheng Lixin, Li Jianhua and Nan Chaoxun, Gateaux and Frechet differentiability of continuous gauges on Banach spaces, Adv. in Math, 20(1991), 326–333.

    MATH  Google Scholar 

  74. Cheng Lixin, Two notes on the smoothensss of Banch spaces, J. Math. Res. Exp. 9(1989), 315–316.

    MATH  Google Scholar 

  75. Cheng Lixin, Smoothness and strong smoothness of Banach spaces, J. Jianghan Petro. Inst. (1) 11(1989), 102–107.

    Google Scholar 

  76. Cheng Lixin and Wei Wenzhan, Some differentiability properties of continuous convex Functions on Banach spaces, J. Guanxi Univ. (1) 16(1991), 65–70.

    Google Scholar 

  77. Cheng Lixin, Differentiability of convex functions and Asplund spaces, Acta. Math. Sci. (1) 15(1995).

    Google Scholar 

  78. Wu Congxin and Cheng Lixin, On weak Asplund spaces, to appear.

    Google Scholar 

  79. Wu Congxin and Cheng Lixin, Differentiability of convex functions on locally convex spaces, J. Harbin Inst, of Tech., E-l, 1(1994), 7–12.

    Google Scholar 

  80. ---, ---, Approximation of functions on metric spaces and its application to differentiability of convex functions on meager sets, Wuhan Univ. Press, 1995.

    Google Scholar 

  81. Li Ronglu and C. Swartz, K-convergence and the Orlicz-Pettis theorem, publ. De’Inst. Math, Tome 49(63), 1991, 117–122.

    Google Scholar 

  82. ---, ---, Spaces for which the uniform convergence principle holds, Studia Sci. Math. Hungarica, 27(1992), 373–384.

    Google Scholar 

  83. ---, ---, A nonlinear Schur theorem, Acta Sci. Math, to appear.

    Google Scholar 

  84. ---, --- and Cho Min-Hyung, Abstract duality, to appear.

    Google Scholar 

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© 1996 Kluwer Academic Publishers

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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

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  • DOI: https://doi.org/10.1007/978-94-009-0185-8_17

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