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Homomorphisms from C*‐algebras
Author(s) -
Sinclair Allan M.
Publication year - 1976
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/plms/s3-32.2.322-s
Subject(s) - homomorphism , mathematics , subalgebra , completeness (order theory) , gödel's completeness theorem , pure mathematics , domain (mathematical analysis) , discrete mathematics , matrix (chemical analysis) , algebra over a field , mathematical analysis , chemistry , chromatography
There is an error in the proof of Theorem 4.1(ii) of the above paper. The error occurs in the sentence ‘Then μ 0 is continuous by Theorem 3.8 and, by continuity and the completeness of B, lifts to a continuous homomorphism μ from A into B’ (p. 449), in that μ need not be a homomorphism. To conclude that μ preserves products from the corresponding fact for μ 0 one needs to know that the domain of μ 0 is a subalgebra of A. The domain of μ 0 will be a subalgebra of A if a 1 ,…,a n can be chosen in A so that Ca 1 ⊕…⊕Ca n ⊕ sp(T.T − + T − .T) is a dense subalgebra of A. It is proved that such a choice of a 1 ,…,a n is possible in a more general situation than this in a paper by K. B. Laursen and A. M. Sinclair, ‘Lifting matrix units in C*‐algebras II’, submitted to Math. Scand.