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Let be a commuting n-tuple of operators on a Hilbert space , and let be its canonical joint polar decomposition (i.e. ⁎ ⁎ , a joint partial isometry, and ). The spherical Aluthge transform of T is the (necessarily commuting) n-tuple . We prove that , where denotes the Taylor spectrum. We do this in two stages: away from the origin, we use tools and techniques from criss-cross commutativity; at the origin, we show that the left invertibility of T or implies the invertibility of P. As a consequence, we can readily extend our main result to other spectral systems that rely on the Koszul complex for their definitions.


© 2019 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved. Original published version available at

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Comptes Rendus Mathematique



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Mathematics Commons



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