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The Primitive Ideal Space of a C*-Algebra

Published online by Cambridge University Press:  20 November 2018

John Dauns
John Dauns*
Affiliation:
Tulane University, New Orleans, Louisiana
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The commutative Gelfand-Naimark Theorem says that any commutative C*-algebra A is isomorphic to the ring C0(M, C) of all continuous complex-valued functions tending to zero outside of compact sets of a locally compact Hausdorff space M. A very important part of this theorem is an intrinsic and also a complete characterization of M as exactly the primitive ideal space of A in the hull-kernel (or weak-star) topology. In the non-commutative case, A ≌ Γ0(M, E)—the ring of sections tending to zero outside of compact subsets of a locally compact Hausdorff space M with values in the stalks or fibers E.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 42 - 49
Copyright
Copyright © Canadian Mathematical Society 1974

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