Local Automorphisms of Operator Algebras on Fr´echet Spaces

• Main Authors: Jung-Hui Liu, 劉榮惠
• Other Authors: Ngai-Ching Wong
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/21194795721134047314

碩士 === 國立中山大學 === 應用數學系研究所 === 91 === 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.