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An extension of Mackey's method to Banach *-algebraic bundles

Author: J M G Fell
Publisher: Providence, R.I. : American Mathematical Society, 1969.
Series: Memoirs of the American Mathematical Society, no. 90.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The main object of the present memoir is to show that the methods and results of Mackey (1958) and Blattner (1963) on the group extension representation problem go through without any essential change in the larger context of homogeneous Banach *-algebraic bundles (with enough cross sections). In order to dispense with separability we shall follow the topological methods of Blattner rather than Mackey's more  Read more...
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Additional Physical Format: Online version:
Fell, J.M.G. (James Michael Gardner), 1923-
Extension of Mackey's method to Banach *-algebraic bundles.
Providence, American Mathematical Society, 1969
(OCoLC)654682934
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: J M G Fell
ISBN: 0821812904 9780821812907
OCLC Number: 1318857
Description: 168 pages ; 26 cm.
Contents: Introduction --
Part I ; Banach bundles --
Integration in Banach bundles over locally compact spaces --
Banach *-algebraic bundles --
Multipliers --
The strong topology of the multiplier bundle --
Homogeneous Banach *-algebraic bundles --
Representations --
The cross-sectional algebra --
The structure of homogeneous Banach *-algebraic bundles --
Examples --
Part II ; Induced representations --
Inducing in stages --
Systems of imprimitivity --
The imprimitivity algebra --
The imprimitivity theorem --
The bundle generalization of the Mackey-Blattner "subgroup analysis" --
The Mackey obstruction ; final results --
Appendix. The Glimm projection-valued measure.
Series Title: Memoirs of the American Mathematical Society, no. 90.
Responsibility: by J.M.G. Fell.

Abstract:

The main object of the present memoir is to show that the methods and results of Mackey (1958) and Blattner (1963) on the group extension representation problem go through without any essential change in the larger context of homogeneous Banach *-algebraic bundles (with enough cross sections). In order to dispense with separability we shall follow the topological methods of Blattner rather than Mackey's more detailed measure-theoretic analysis. Except for the last section, Part II of this memoir is in fact a rewriting of much of Blattner's papers (1963), making the modifications necessary in the larger context of bundles. The last Section 17 gives an account of the 'Mackey obstruction' in the nonseparable case, leading to an analogue (Theorem 17.2) of Theorem 8.2 of Mackey's paper for homogeneous Banach *-algebraic bundles, without separability restrictions. This is the culminating point of the present memoir.

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