@article {
author = {Anjidani, E.},
title = {Almost multiplicative linear functionals and approximate spectrum},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {1},
pages = {177-187},
year = {2015},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
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.},
keywords = {almost multiplicative linear functional,Ransford spectrum,pseudospectrum,condition spectrum,Gleason-Kahane-Zelazko theorem},
url = {http://bims.iranjournals.ir/article_596.html},
eprint = {http://bims.iranjournals.ir/article_596_bec59d33577ac7d73d2c66407e9eec46.pdf}
}