Vol. 25, No. 3, 1968

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The structure space of a commutative locally m-convex algebra

Robert Morgan Brooks

Vol. 25 (1968), No. 3, 443–454

If A is a commutative Banach algebra with identity, then the sets (all maximal ideals), c (all closed maximal ideals), 1 (kernels of nonzero C-valued homomorphisms of A), and 0 (kernels of nonzero continuous C-valued hommorphisms of A) coincide. If A is a commutative complete locally m-convex algebra, one has only c = 0 ⊂ℳ1 ⊂ℳ, and the containments can be proper. Our goal is to investigate and its relationship to 0; specifically (1) to give a description of (A) in terms of A and 0(A) which is valid for at least the class of F-algebras, (2) to determine when (A) is one of the standard compactifications (Wallman, Stone-Čech) of 0(A).

Mathematical Subject Classification
Primary: 46.55
Received: 22 September 1966
Published: 1 June 1968
Robert Morgan Brooks