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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Representations of a class of real $B^ *$-algebras as algebras of quaternion-valued functions
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by S. H. Kulkarni PDF
Proc. Amer. Math. Soc. 116 (1992), 61-66 Request permission


For a compact Hausdorff space $X$, let $C(X,{\mathbf {H}})$ denote the set of all quaternion-valued functions on $X$. It is proved that if a real ${B^*}$-algebra $A$ satisfies the following conditions: (i) the spectrum of every selfadjoint element is contained in the real line and (ii) every element in $A$ is normal, then $A$ is isometrically $*$-isomorphic to a closed $*$-subalgebra of $C(X,{\mathbf {H}})$ for some compact Hausdorff $X$. In particular, a real ${C^*}$-algebra in which every element is normal is isometrically $*$-isomorphic to a closed $*$-subalgebra of $C(X,{\mathbf {H}})$.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 61-66
  • MSC: Primary 46K05; Secondary 46L05
  • DOI:
  • MathSciNet review: 1110546