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Let A be an algebra. A mapping : A ! A is called a 2-local automorphism if for
every a, b in A there is an automorphism ab : A ! A, depending on a and b, such
that ab(a) = (a) and ab(b) = (b). Here no linearity, surjectivity or continuity of
is assumed. In this thesis we extend a result of Lajos Moln´ar stating that every
2-local automorphism of an operator algebra on a Banach space with a Schauder basis
is an automorphism. We obtain the same conclusion for operator algebras on Fr´echet
spaces with Schauder bases.

Contents
1 Introduction 1
2 Preliminary Results 2
3 Main results 7
References 18

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