@MISC{LOPBAN12.MIZ,
  AUTHOR = {Nakasho, Kazuhisa},
  TITLE = {Isomorphisms from the Space of Multilinear Operators},
  SECTION1 = {Plain Isomorphisms from the Space of Multilinear Operators},
  SECTION2 = {Extensions to Isometric Isomorphism from the Normed Space of Multilinear Operators},
  DAY = {27},
  MONTH = {May},
  YEAR = {2019},
  ADDRESS1 = {Yamaguchi University\\Yamaguchi, Japan},
  MSC2010 = {46-00 47A07 47A30},
  KEYWORDS = {Linear Operators; Bilinear operators; Multilinear Operators; Isomorphism of Linear Operator Spaces},
  SUMMARY = {In this article, the isomorphisms from the space of
     multilinear operators are discussed.
    In the first chapter, two isomorphisms are formalized.
    The former isomorphism shows the correspondence between the space
    of multilinear operators and the space of bilinear operators.
    The latter shows the correspondence between the space of
    multilinear operators and the space of the composition of linear
    operators.
    In the last chapter, the above isomorphisms are extended to
    isometric mappings between the normed spaces.
    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}
}
