@MISC{LOPBAN_8.MIZ,
  AUTHOR = {Nakasho, Kazuhisa and Futa, Yuichi and Shidama, Yasunari},
  TITLE = {Continuity of Bounded Linear Operators on Normed Linear Spaces},
  SECTION1 = {Uniform Continuity and Lipschitz Continuity of Bounded Linear Operators},
  SECTION2 = {Basic Properties of Currying},
  SECTION3 = {Equivalence of Some Definitions of Continuity of Bilinear Operators},
  DAY = {29},
  MONTH = {September},
  YEAR = {2018},
  ADDRESS1 = {Yamaguchi University\\Yamaguchi, Japan},
  ADDRESS2 = {Tokyo University of Technology\\Tokyo, Japan},
  ADDRESS3 = {Shinshu University\\Nagano, Japan},
  MSC2010 = {46-00 47A07 47A30},
  KEYWORDS = {Lipschitz continuity; Uniform continuity; Bounded linear operators; Bilinear operators},
  SUMMARY = {In this article, we discuss on the continuity of bounded linear operators on normed linear    spaces.
            In the first section, it is discussed that bounded linear operators on normed linear spaces are    uniformly continuous and Lipschitz continuous.
            Especially, a bounded linear operator on the dense subset of a complete normed linear space has   a unique natural extension over the whole space.
            In the next section, several basic currying properties are formalized.
            In the last section, we formalized that continuity of bilineaer operator is equivalent to both   Lipschitz continuity and local continuity.
            We referred to \cite{miyadera:1972}, \cite{yoshida:1980}, and \cite{Dunford:1958} in this   formalization.},
  ACKNOWLEDGEMENT = {This study was supported in part by JSPS KAKENHI Grant Number JP17K00182.}}

@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}
