The Density Of Generalized Inverses Of M_n(A) In Banach Algebras

In this thesis, we generalize some results which are known in C*-algebras to Banach algebras. In this thesis let A always be a unital Banach algebra. The author proves the following results:（1） If the set of generalized inverses in M_n（A） is dense in M_n（A）, then the set of generalized inverses in A is dense in A.（2） Let p, q be non-zero idempotents in A, if the set of generalized inverses in. pAp is dense in pAp, then the set of generalized inverses in M₂（A） is dense in M2（A）.（3） The density of generalized inverses in ideals and quotients of Banach al-gebras in which the set of generalized inverses is dense.（4） Lift a generalized inverse from quotient Banach algebras.