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Type 2 Semi‐Algebras of Continuous Functions
Author(s) -
Bonsall F. F.
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012533
Subject(s) - mathematics , tensor product , hausdorff space , type (biology) , pure mathematics , cone (formal languages) , characterization (materials science) , mathematics subject classification , continuous function (set theory) , product (mathematics) , space (punctuation) , function (biology) , algebra over a field , geometry , nanotechnology , ecology , linguistics , philosophy , materials science , algorithm , evolutionary biology , biology
A semi‐algebra of continuous functions is a cone A of continuous real functions on a compact Hausdorff space X such that A contains the products of its elements. A cone A is said to be of type n if f ∈ A implies f n (1 + f ) −1 ∈ A . Uniformly closed semi‐algebras of types 0 and 1 have long been characterized in a manner analogous to the Stone–Weierstrass theorem, but, except for the case when A is generated by a single function, little has been known about type 2. Here, progress is reported on two problems. The first is the characterization of those continuous linear functionals on C ( X ) that determine semi‐algebras of type 2. The second is the determination of the type of the tensor product of two type 1 semi‐algebras. 1991 Mathematics Subject Classification : 46J10.