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An Extension of Mackey's Method to Banach *-Algebraic Bundles

James Michael Gardner Fell

出版	American Mathematical Soc., 1969
ISBN	08218129049780821812907
URL	http://books.google.com.hk/books?id=N8jTCQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.