@MISC{LOPBAN10.MIZ,
  AUTHOR = {Nakasho, Kazuhisa},
  TITLE = {Multilinear Operator and Its Basic Properties},
  SECTION1 = {Multilinear Operator on Real Linear Spaces},
  SECTION2 = {Bounded Multilinear Operator on Normed Linear Spaces},
  DAY = {27},
  MONTH = {February},
  YEAR = {2019},
  ADDRESS1 = {Yamaguchi University\\Yamaguchi, Japan},
  MSC2010 = {46-00 47A07 47A30},
  KEYWORDS = {Lipschitz continuity; Bounded linear operators; Bilinear operators; Algebraic structure; Banach Spaces},
  SUMMARY = {In the first chapter, the notion of multilinear operator on real linear spaces is discussed. 
  The algebraic structure of multilinear operators is introduced here.
  In the second chapter, the results of the first chapter are extended to the case of the normed spaces.
  This chapter shows the bounded multilinear operators on normed linear spaces constitutes the algebraic   structure.
  We referred to \cite{miyadera:1972}, \cite{yoshida:1980}, \cite{Schwartz1997a}, \cite{Schwartz1997b} in   this formalization.},
  ACKNOWLEDGEMENT = {I would like to express my gratitude to Professor Yasunari Shidama for his helpful   advice.}}

@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}
}
