Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles
Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles

Author: J. M.G. Fell

Publisher: Academic Press

Published: 1988-05-01

Total Pages: 755

ISBN-13: 0080874452

DOWNLOAD EBOOK

This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Non-Commutative Spectral Theory for Affine Function Spaces on Convex Sets
Non-Commutative Spectral Theory for Affine Function Spaces on Convex Sets

Author: Erik Magnus Alfsen

Publisher: American Mathematical Soc.

Published: 1976

Total Pages: 136

ISBN-13: 0821818724

DOWNLOAD EBOOK

In this paper we develop geometric notions related to self-adjoint projections and one-sided ideals in operator algebras. In the context of affine function spaces on convex sets we define projective units. P-projections, and projective faces which generalize respectively self-adjoint projections p, the maps a [right arrow] pap, and closed faces of state spaces of operator algebras. In terms of these concepts we state a "spectral axiom" requiring the existence of "sufficiently many" projective objects. We then prove the spectral theorem: that elements of the affine function space admit a unique spectral decomposition. This in turn yields a satisfactory functional calculus, which is unique under a natural minimality requirement (that it be "extreme point preserving").