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  • 1 8 Redwood Grove, Northfields Avenue Ealing, London W5 4SZ England, UK
  • 2 Catholic University of Rio de Janeiro 22453-900 Rio de Janeiro RJ Brazil
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Let T and S be Hilbert space operators such that Weyl’s theorem holds for both of them. In general, it does not follow that Weyl’s theorem holds for the direct sum TS . We give asymmetric sufficient conditions on T and S to ensure that the direct sum TS satisfies Weyl’s theorem. It is assumed that just one of the direct summands satisfies Weyl’s theorem but is not necessarily isoloid, while the other has no isolated points in its spectrum.

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