Vol. 109, No. 1, 1983

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Sectional representations of Banach modules

Joseph Weston Kitchen, Jr. and David A. Robbins

Vol. 109 (1983), No. 1, 135–156

This paper is concerned with the representation of Banach algebras and Banach modules as sections of bundles of Banach spaces. In particular: (1) if A is a commutative Banach algebra, then A may be represented by sections of a locally trivial canonical line bundle; (2) if A is a Banach algebra which is represented as sections of a canonical bundle of Banach algebras, then there is a natural way in which any Banach module M over A can be represented by sections of a canonical bundle of Banach modules over the corresponding algebra bundle. We also investigate projective tensor products of bundles of Banach algebras and bundles of Banach modules.

Mathematical Subject Classification 2000
Primary: 46H25
Secondary: 46M20
Received: 10 September 1981
Revised: 4 March 1982
Published: 1 November 1983
Joseph Weston Kitchen, Jr.
David A. Robbins