TY - JOUR
ID - 466
TI - Module approximate amenability of Banach algebras
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Pourmahmood-Aghababa, H.
AU - Bodaghi, A.
AD - Tabriz University, Tabriz, Iran
AD - Islamic Azad University of Garmsar, Garmsar, Iran
Y1 - 2013
PY - 2013
VL - 39
IS - 6
SP - 1137
EP - 1158
KW - Module derivation
KW - Module amenability
KW - Approximately inner
KW - Inverse semigroups
DO -
N2 - In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same properties. It is also shown that module uniform approximate (contractibility) amenability and module (contractibility, respectively) amenability for commutative Banach modules are equivalent. Applying these results to l^1 (S) as an l^1 (E)-module, for an inverse semigroup S with the set ofidempotents E, it is shown that l^1(S) is module approximately amenable (contractible) if and only if it is module uniformly approximately amenable if and only if S is amenable.Moreover, l^1(S)^{**} is module (uniformly) approximately amenable if and only if an appropriate group homomorphic image of S is finite.
UR - http://bims.iranjournals.ir/article_466.html
L1 - http://bims.iranjournals.ir/article_466_605a2ac8ad2936a6371f9bda251cbb65.pdf
ER -