be a commutative Banach algebra with dual
, and call
is an algebra in which approximately multiplicative functionals are near multiplicative (AMNM) if for each
, there is
-multiplicative. The author studies these entities and shows that AMNM algebras include the well-known examples (finite dimensional,
, disc algebra), but not all. A result of Gleason about multiplicativeness of functions with range contained in the spectrum is studied in a more general context.