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On complex strict and uniform convexity


Author: J. Globevnik
Journal: Proc. Amer. Math. Soc. 47 (1975), 175-178
DOI: https://doi.org/10.1090/S0002-9939-1975-0355564-9
MathSciNet review: 0355564
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Abstract | References | Additional Information

Abstract: Strict and uniform $ c$-convexity of complex normed spaces are introduced as a natural generalization of strict and uniform convexity. It is proved that the complex space $ {L_1}(S,\sigma ,\mu )$ is uniformly $ c$-convex. An application to analytic functions is given.


References [Enhancements On Off] (What's this?)

  • [1] L. A. Harris, Schwarz's lemma in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 1014-1017. MR 43 #936. MR 0275179 (43:936)
  • [2] -, A continuous form of Schwarz's lemma in normed linear spaces, Pacific J. Math. 38 (1971), 635-639. MR 46 #4167. MR 0305037 (46:4167)
  • [3] E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R.I., 1957. MR 19, 664. MR 0089373 (19:664d)
  • [4] G. Köthe, Topologische lineare Räume. I, 2nd ed., Die Grundlehren der math. Wissenschaften, Band 107, Springer-Verlag, Berlin, 1966; English transl., Die Grundlehren der math. Wissenschaften, Band 159, Springer-Verlag, New York, 1969. MR 33 #3069; 40 #1750.
  • [5] D. Pizanelli, Applications analytiques en dimension infinie, Bull. Sci. Math. 96 (1972), 181-191. MR 0331061 (48:9396)
  • [6] E. Thorp and R. Whitley, The strong maximum modulus theorem for analytic functions into a Banach space, Proc. Amer. Math. Soc. 18 (1967), 640-646. MR 35 #5643. MR 0214794 (35:5643)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355564-9
Keywords: Analytic functions, maximum modulus theorem, strictly and uniformly convex spaces
Article copyright: © Copyright 1975 American Mathematical Society

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