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Strong Uniqueness of the Functional Calculus for Some Commutative Banach Algebras
Author(s) -
Zame William R.
Publication year - 1976
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-13.1.13
Subject(s) - uniqueness , mathematics , homomorphism , commutative property , banach algebra , simple (philosophy) , pure mathematics , identity (music) , ideal (ethics) , functional calculus , algebra over a field , banach space , mathematical analysis , law , philosophy , physics , epistemology , political science , acoustics
A commutative Banach algebra with identity is said to be quasi‐simple if 0 is the only element which belongs to every power of every maximal ideal. A strong uniqueness result is established for the functional calculus in quasi‐simple algebras with no non‐trivial idempotents. Related results on uniqueness and continuity of homomorphisms are also obtained.