@MISC{LOPBAN_9.MIZ,
  AUTHOR = {Nakasho, Kazuhisa},
  TITLE = {Bilinear Operators on Normed Linear Spaces},
  SECTION1 = {Real Vector Space of Bilinear Operators},
  SECTION2 = {Real Normed Linear Space of Bounded Bilinear Operators},
  SECTION3 = {Real Banach Space of Bounded Bilinear Operators},
  SECTION4 = {Isomorphic Mappings between the Space of Bilinear Operators and the Space of Composition of Linear Operators},
  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 = {The main topic of this article is the property of bilinear operator on normed linear spaces. 
    In the first two chapters, algebraic structures of bilinear operators on linear spaces are formalized.
    Especially, the space of bounded bilinear operators on normed linear spaces is discussed here.
    In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space.
    In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is formalized.
    We referred to \cite{miyadera:1972}, \cite{yoshida:1980}, \cite{Dunford:1958}, \cite{Schwartz1997a} and \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}
}