Department of Mathematics, University of Neyshabur
Abstract
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.
Anjidani, E. (2015). Almost multiplicative linear functionals and approximate spectrum. Bulletin of the Iranian Mathematical Society, 41(1), 177-187.
MLA
Anjidani, E. "Almost multiplicative linear functionals and approximate spectrum", Bulletin of the Iranian Mathematical Society, 41, 1, 2015, 177-187.
HARVARD
Anjidani E. (2015). 'Almost multiplicative linear functionals and approximate spectrum', Bulletin of the Iranian Mathematical Society, 41(1), pp. 177-187.
CHICAGO
E. Anjidani, "Almost multiplicative linear functionals and approximate spectrum," Bulletin of the Iranian Mathematical Society, 41 1 (2015): 177-187,
VANCOUVER
Anjidani E. Almost multiplicative linear functionals and approximate spectrum. BIMS. 2015;41(1):177-187.
