TY - JOUR ID - 596 TI - Almost multiplicative linear functionals and approximate spectrum JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Anjidani, E. AD - Department of Mathematics, University of Neyshabur Y1 - 2015 PY - 2015 VL - 41 IS - 1 SP - 177 EP - 187 KW - almost multiplicative linear functional KW - Ransford spectrum KW - pseudospectrum KW - condition spectrum KW - Gleason-Kahane-Zelazko theorem DO - N2 - We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is a linear functional with ϕ(a)∈σ_δ (a) for all a∈A, then ϕ is ε-almost multiplicative. Finally, we use these ideas to provide a sufficient condition for a δ-almost multiplicative functional to be multiplicative. UR - http://bims.iranjournals.ir/article_596.html L1 - http://bims.iranjournals.ir/article_596_bec59d33577ac7d73d2c66407e9eec46.pdf ER -