Perturbation Analysis Of Group Inverses In Ωp-banach Algebras

In this paper we mainly gave the definition of stable perturbation on Ωp-unital Banach algebras,also found the upper bound for the change of the group inverse and the Drazin inverse,and then applied them onto the perturbation analysis of group inverse and Drazin in-verse of bounded linear operators on Ωp-Banach spaces.What’s more,we found the reason that we can’t prove the spectrums of elements in Cp-unital Banach algebras are non-empty by classical methods and gave the concrete instances showed that the spectrums of elements in Cp-unital Banacth algebras may be empty,even if there is elemen-t whose spectrum is not empty,it may not be compact.However,despite of these facts,we proved that several important families of Cp-valued functions formed into Cp-Banach algebras under the usual operations and norm,and we can write out the spectrums of these functions accurately.We also showed that there is no natural inner product on finite dimensional Cp-vector spaces by studying the linear forms on Cp-vector spaces,thus there is no C*-algebras on Cp.