@MISC{LOPBAN11.MIZ,
  AUTHOR = {Nakasho, Kazuhisa and Shidama, Yasunari},
  TITLE = {Continuity of Multilinear Operator on Normed Linear Spaces},
  SECTION1 = {Completeness of the Space of Multilinear Operators},
  SECTION2 = {Equivalence of Continuity Definition of Multilinear Operator},
  DAY = {27},
  MONTH = {February},
  YEAR = {2019},
  ADDRESS1 = {Yamaguchi University\\Yamaguchi, Japan},
  ADDRESS2 = {Shinshu University\\Nagano, Japan},
  MSC2010 = {46-00 47A07 47A30},
  KEYWORDS = {Lipschitz continuity; Bounded linear operators; Multilinear operators; Banach Space},
  SUMMARY = {In this article, the continuity definitions of multilinear operators on normed linear spaces are discussed.
  In the first chapter, several basic theorems are prepared to handle the norm of the multilinear operator,
  and then it is formalized that the completeness of the linear space of bounded multilinear operators that range is a Banach space.
  In the last chapter, the continuity of the multilinear operator on finite normed spaces is addressed.
  Especially, it is formalized that the continuity at the origin can be extended to the continuity at every point in its whole domain here.
  We referred to \cite{miyadera:1972}, \cite{yoshida:1980}, \cite{Schwartz1997a}, \cite{Schwartz1997b} in this formalization.}}

@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}

@BOOK{Schwartz1997a,
  TITLE={Th\'{e}orie des ensembles et topologie, tome 1. Analyse},
  AUTHOR={Laurent Schwartz},
  PUBLISHER={Hermann},
  YEAR={1997},
  MONTH={10},
}

@BOOK{Schwartz1997b,
  TITLE = {Calcul diff\'{e}rentiel, tome 2. Analyse},
  AUTHOR = {Laurent Schwartz},
  PUBLISHER = {Hermann},
  YEAR = {1997},
  MONTH = {10}}
