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Are All Uniform Algebras Amnm?
Author(s) -
Sidney Stuart J.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002585
Subject(s) - mathematics , multiplicative function , banach algebra , mathematics subject classification , commutative property , pure mathematics , division algebra , algebra over a field , property (philosophy) , construct (python library) , algebra representation , banach space , mathematical analysis , philosophy , programming language , epistemology , computer science
A Banach algebra a is AMNM if whenever a linear functional φ on a and a positive number δ satisfy |φ( ab )−φ( a )φ( b )|⩽δ‖ a ‖·‖ b ‖ for all a , b ∈ a, there is a multiplicative linear functional ψ on a such that ‖φ−ψ‖= o (1) as δ→0. K. Jarosz [ 1 ] asked whether every Banach algebra, or every uniform algebra, is AMNM. B. E. Johnson [ 3 ] studied the AMNM property and constructed a commutative semisimple Banach algebra that is not AMNM. In this note we construct uniform algebras that are not AMNM. 1991 Mathematics Subject Classification 46J10.