Premium
Duality between Locally m‐Convex Algebras and Completely Regular Spaces
Author(s) -
ROSA DOMENICO
Publication year - 1995
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1995.tb55908.x
Subject(s) - mathematics , hausdorff space , pure mathematics , functor , tychonoff space , compact open topology , subcategory , locally compact space , duality (order theory) , covariance and contravariance of vectors , locally convex topological vector space , category of topological spaces , commutative property , topological space , topological tensor product , functional analysis , biochemistry , chemistry , gene
It is well known that, for the category B of commutative Banach algebras and the category CH of compact Hausdorff spaces, the contravariant functors M: B → CH and C: CH → B are adjoint on the right. This adjoint situation is extended to the category of completely regular spaces and the subcategory consisting of all locally m ‐convex algebras A whose Gelfand map A → CM(A) (compact‐open topology) is continuous. An analogous extension is obtained for the dual equivalence (Gelfand duality) between B *‐algebras and compact Hausdorff spaces.