Kulkarni, S.H.Sukumar, D.2020-03-312020-03-312010Studia Mathematica, 2010, Vol.197, 1, pp.93-9910.4064/sm197-1-8https://idr.nitk.ac.in/handle/123456789/9836Let A be a complex commutative Banach algebra with unit 1 and ? > 0. A linear map ?: A ?C is said to be ?-almost multiplicative if |?(ab) - ? (a) ? (b)| ? ?abfor all a, b ? A. Let 0 < e < 1. The e-condition spectrum of an element a in A is defined by ?e.(a) := {? ? C:?-a?- a-1? 1/e} with the convention that?- a(? - a)-1= ? when ? - a is not invertible. We prove the following results connecting these two notions: (1) If ?(1) = 1 and ? is ?-almost multiplicative, then ?(a) ? ?e(a) for all a in A.then (2) If ?is lenear and ?(a) ??e(a) for all a in A ,then ?-is ? almost multiplicative for some ?. The first result is analogous to the Gelfand theory and the last result is analogous to the classical Gleason-Kahane- ?elazko theorem.Article