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Similarity implies homotopy of idempotents in Banach algebras of stable rank one

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Abstract.

We establish the property stated in the title by means of an elementary construction: in a Banach algebra of stable rank one, any two similar idempotents can be connected by a piecewise affine path of idempotents consisting of at most 3 affine steps.

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  1. Department of Mathematics, Texas A&M University, College Station, Mailstop 3368, TX, 77843-3368, USA

    Julien Giol

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  1. Julien Giol
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Correspondence to Julien Giol.

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Received: 1 February 2006

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Giol, J. Similarity implies homotopy of idempotents in Banach algebras of stable rank one. Arch. Math. 88, 235–238 (2007). https://doi.org/10.1007/s00013-006-1891-7

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  • DOI: https://doi.org/10.1007/s00013-006-1891-7

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