@MISC{LOPBAN_7.MIZ,
  AUTHOR = {Sakurai, Hideki and Okazaki, Hiroyuki and Shidama, Yasunari},
  TITLE = {Banach's Continuous Inverse Theorem and Closed Graph Theorem},
  NOTE = {This work was supported by JSPS KAKENHI 22300285.},
  DAY = {6},
  MONTH = {August},
  YEAR = {2012},
  ADDRESS1 = {406-3, Haneo, Naganohara, Agatuma, Gunma, Japan},
  ADDRESS2 = {Shinshu University\\4-17-1 Wakasato, Nagano, Japan},
  ADDRESS3 = {Shinshu University\\4-17-1 Wakasato, Nagano, Japan},
  SUMMARY = {In this article we formalize one of the most important
             theorems of linear operator theory -- the Closed Graph Theorem
             commonly used in a standard text book such as
             \cite{miyadera:1972} in Chapter 24.3.
             It states that a surjective closed linear operator between
             Banach spaces is bounded.}}

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

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

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