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Fundamental Concepts and Propositions in the Theory of Normed Algebras

  • M. A. Naimark

Abstract

We shall say that R is a linear algebra if:
  1. 1)

    R is a linear space;

     
  2. 2)

    an operation of multiplication (which in general is not commutative) is defined in R satisfying the following conditions: a) α(xy) = (αx)y = x(αy), b) (xy)z = x(yz), c) (x+y)z = xz+yz, d) x(y+z) = xy + xz for arbitrary x, y, zR and any number α.

     

Keywords

Banach Algebra Left Ideal Division Algebra Continuous Homomorphism Topological Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Wolters-Noordhoff Publishing, Groningen, The Netherlands 1972

Authors and Affiliations

  • M. A. Naimark
    • 1
  1. 1.Steklov Institute of MathematicsAcademy of SciencesU.S.S.R.

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