@MISC{LOPBAN_5.MIZ,
  AUTHOR = {Sakurai, Hideki and Kunimune, Hisayoshi and Shidama, Yasunari},
  TITLE = {Uniform Boundedness Principle},
  SECTION1 = {Uniform Boundedness Principle},
  SECTION2 = {Banach-Steinhaus Theorem},
  DAY = {9},
  MONTH = {October},
  YEAR = {2007},
  ADDRESS1 = {Graduate School of Science and Technology\\Shinshu University\\4-17-1 Wakasato, Nagano, Japan},
  ADDRESS2 = {Faculty of Engineering\\Shinshu University\\4-17-1 Wakasato, Nagano, Japan},
  ADDRESS3 = {Faculty of Engineering\\Shinshu University\\4-17-1 Wakasato, Nagano, Japan},
  SUMMARY = {In this article at first, we proved the lemma of
         the inferior limit and the superior limit.
         Next, we proved the Baire category theorem (Banach space version)
         \cite{yoshida:1980}, \cite{miyadera:1972}, \cite{Dunford:1958},
         quoted them and proved the uniform boundedness principle.
         Moreover, it added the proof of the Banach-Steinhaus theorem.}}

@BOOK{yoshida:1980,
 AUTHOR={Kosaku Yoshida},
 TITLE={Functional Analysis},
 PUBLISHER={Springer},
 YEAR=1980}

@BOOK{miyadera:1972,
 AUTHOR={Isao Miyadera},
 TITLE={Functional Analysis},
 PUBLISHER={Riko-Gaku-Sya},
 YEAR=1972}

@BOOK{Dunford:1958,
 AUTHOR={N.Dunford J and T.Schwartz},
 TITLE={Linear operators I},
 PUBLISHER={Interscience Publ.},
 YEAR=1958}
