| This thesis has two parts. The first part deals with some questions in amenability. We show that for a Banach algebra A with a bounded approximate identity, the amenability of A ⊗&d14; A, the amenability of A ⊗&d14; Aop and the amenability of A are equivalent. Also if A is a closed ideal in a commutative Banach algebra B, then the (weak) amenability of A ⊗&d14; B implies the (weak) amenability of A.;The second part deals with questions in generalized notions of amenability such as approximate amenability and bounded approximate amenability. First we prove some new results about approximately amenable Banach algebras. Then we state a characterization of approximately amenable Banach algebras and a characterization of boundedly approximately amenable Banach algebras.;Finally, we prove that B(lp( E)) is not approximately amenable for Banach spaces E with certain properties. As a corollary of this part, we give a new proof that B(l2) is not approximately amenable.;Finally, we show that if the Banach algebra A is amenable through multiplication pi, then A is also amenable through any multiplication rho such that ||rho - pi|| < 111 . |
