Normed Rings and Spectral Representation

  • Kôsaku Yosida
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 123)

Abstract

A linear space A over a scalar field (F) is said to be an algebra or a ring over (F), if to each pair of elements x, y ∈ A a unique product xyA is defined with the properties:
$$\left. {\begin{array}{*{20}{c}} {(xy)z = x(yz)\;(associativity),} \\ {x(y + z) = xy + xz\;(distributivity),} \\ {\alpha \beta (xy) = (\alpha x)(\beta y)} \\ \end{array} } \right\}$$
(1)
.

Keywords

Hull Tral Topo Itan 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1965

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.University of TokyoJapan

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