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Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras
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Jean Marion
Published/Copyright:
February 23, 2010
Abstract
We consider a wide class of unital involutive topological algebras provided with a C*-norm and which are inverse limits of sequences of unital involutive Banach algebras; these algebras are taking a prominent position in noncommutative differential geometry, where they are often called unital smooth algebras. In this paper we prove that the group of invertible elements of such a unital solution smooth algebra and the subgroup of its unitary elements are regular analytic Fréchet–Lie groups of Campbell–Baker–Hausdorff type and fulfill a nice infinite-dimensional version of Lie's second fundamental theorem.
Key words and phrases.: Unital involution; ILB-algebra; strong ILB–Lie group; CBH–Lie group; Lie's second fundamental theorem; Fréchet–Lie group
Received: 1994-03-01
Published Online: 2010-02-23
Published in Print: 1995-August
© 1995 Plenum Publishing Corporation
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- Global Dimensions of Subidealizer Rings
- Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras
Keywords for this article
Unital involution;
ILB-algebra;
strong ILB–Lie group;
CBH–Lie group;
Lie's second fundamental theorem;
Fréchet–Lie group
Articles in the same Issue
- On Optimal Stopping of Inhomogeneous Standard Markov Processes
- Geometry of Poisson Structures
- Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. I
- On the Solvability of A Spatial Problem of Darboux Type for the Wave Equation
- On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument
- Global Dimensions of Subidealizer Rings
- Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras
