| dc.description.abstract | Most studies on preserver problems have been on linear preserver prob¬lems (LPPs) in matrix theory. It is known that local derivations of Von Neumann algebras are continuous linear maps, which coincide with some derivation at each point in the algebra over the field of complex numbers. Most of the studies have been focusing on the spectral norm preserver and rank preserver problems of linear maps on matrix algebras but not on norm preserver problems for local automorphism of commutative Banach algebras. In this study, we have investigated properties of local auto¬morphism of commutative Banach algebras and determined their norms. The objectives of the study have been to: Investigate properties of local automorphisms of commutative Banach algebras; establish norm preserv¬ing conditions for local automorphisms of commutative Banach algebras and determine the norms of local automorphisms of commutative Banach algebras. The methodology involved the concept of local automorphisms and derivations introduced by Kadison and Sourour. We used Hahn¬Banach extension theorem, Gelfand transform and the results developed by Molnar to investigate the preserver problems of local automorphisms. The results obtained show that local automorphisms are linear, inner, bounded, continuous and their groups are algebraically reflexive. More¬over, the results on norms indicate that ll<ti(x) + <P(Y)II = llxll + IIYII and ll<Px(Y)II = 2IIYII- The results obtained in this study are useful in the applications of operator algebras and quantum mechanics. | en_US |