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We give estimates for the norm of      e int {e^{\operatorname {int} }}       in      A + / I {A^ + }/I      , where      I I       is a closed ideal of      A + {A^ + }       without inner factor, provided that the hull of      I I       satisfies suitable geometric conditions.

Estimates for inverses of 𝑒^{𝑖𝑛𝑡} in some quotient algebras of 𝐴⁺