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 -