Fundamental Concepts and Propositions in the Theory of Normed Algebras

  • M. A. Naimark


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.



Banach Algebra Left Ideal Division Algebra Continuous Homomorphism Topological Algebra 
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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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