Abstract
It is proved that in Banach algebras generated by two idempotents and, perhaps, by a certain flip operator the standard identity F4 is fulfilled. The maximal ideal space of such algebras is determined and the corresponding symbol is given. By means of local techniques these results are applied to obtain a symbol calculus for singular integral operators with Carleman shift (changing the orientation) in weighted Banach spaces.
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Roch, S., Silbermann, B. Algebras generated by idempotents and the symbol calculus for singular integral operators. Integr equ oper theory 11, 385–419 (1988). https://doi.org/10.1007/BF01202079
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DOI: https://doi.org/10.1007/BF01202079