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Order Completeness in Lipschitz Algebras

✍ Scribed by N. Weaver

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
530 KB
Volume
130
Category
Article
ISSN
0022-1236

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✦ Synopsis

The algebraic properties of Lipschitz spaces have received much attention. This has led to a good understanding of such things as complex homomorphisms and ideals (but not subalgebras) when the underlying metric space is compact. Taking a cue from the recent observation that Lipschitz spaces are order-complete ( (N). Weaver, Pacific J. Math. 164 (1994), 179-193), we here investigate these topics under the hypothesis of order continuity or order closure in place of norm continuity or norm closure. We obtain simple characterizations of order-continuous complex homomorphisms and order-complete subalgebras and ideals, even when the underlying metric space is not compact. In particular, we show that order-complete subalgebras and quotients by order-complete ideals are themselves Lipschitz spaces. is: 1995 Academic Press. Inc

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