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Extensions of endomorphisms of C(X) | | J.F. Feinstein
; T.J. Oliver
; | | Date: |
1 Oct 2004 | | Subject: | Functional Analysis MSC-class: 46J10;47B48 | math.FA | | Abstract: | For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p in C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism of C(X) extends to the Arens-Hoffman extension with respect to p then it also extends to the simple Cole extension with respect to p. We show that the converse to this is false. For locally connected, metric X we characterize the algebraically closed C(X), in terms of the extendability of endomorphisms to Arens-Hoffman and to simple Cole extensions. | | Source: | arXiv, math.FA/0410025 | | Services: | Forum | Review | PDF | Favorites | |
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