@MISC{DUALSP02.MIZ,
  AUTHOR = {Narita, Keiko and Endou, Noboru and Shidama, Yasunari},
  TITLE = {Bidual Spaces and Reflexivity of Real Normed Spaces},
  ACKNOWLEDGEMENT = {This work was supported by JSPS KAKENHI
    22300285 and 23500029.},
  SECTION1 = {The application of Hahn-Banach's Theorem},
  SECTION2 = {Bidual Spaces of Real Normed Spaces},
  SECTION3 = {Uniform Boundedness Theorem for Linear Functionals},
  SECTION4 = {Reflexivity of Real Normed Spaces},
  DAY = {29},
  MONTH = {November},
  YEAR = {2014},
  ADDRESS1 = {Hirosaki-city, Aomori, Japan},
  ADDRESS2 = {Gifu National College of Technology, Gifu, Japan},
  ADDRESS3 = {Shinshu University\\Nagano},
  SUMMARY = {In this article, we treated bidual spaces and
  reflexivity of real normed spaces.
  At the beginning, we proved some corollaries applying Hahn-Banach's
  theorem and showed related theorems by them.
  In the second section, we proved about the norm of dual spaces and
  we defined the natural mapping, from real normed spaces to bidual
  spaces of them. We also proved some properties of this mapping.
  Next, we defined \verb!RNS_Real!, real number spaces as real
  normed spaces and proved related theorems. We can regard
  linear functionals as linear operators by this definition.
  Accordingly we proved Uniform Boundedness Theorem for linear
  functionals using the theorem 5 from \cite{LOPBAN_5.ABS}.
  Finally, we defined reflexivity of real normed spaces and
  proved some theorems about isomorphism of linear operators.
  Using them, we proved some properties about reflexivity.}}

