On an approximate automorphism on a $C^{*}$-algebra

DOI10.1090/S0002-9939-03-07252-6zbMath1055.47032OpenAlexW1547923072MaRDI QIDQ4461159

Chun-Gil Park

Publication date: 29 March 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-03-07252-6

zbMATH Keywords

Banach algebra\(C^*\)-algebraHyers--Ulam--Rassias stabilityapproximate automorphism

Mathematics Subject Classification ID

Linear operators on Banach algebras (47B48) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (26)

Multi-\(C^{*}\)-ternary algebras and applications ⋮ Isometric isomorphisms in proper \(CQ^*\)-algebras ⋮ Isomorphisms between quasi-Banach algebras ⋮ Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces ⋮ On approximate homomorphisms: A fixed point approach ⋮ Stability and superstability of generalized quadratic ternary derivations on non-Archimedean ternary Banach algebras: a fixed point approach ⋮ The \(N\)-isometric isomorphisms in linear \(N\)-normed \(C^{\ast}\)-algebras ⋮ Functional Inequalities in Fuzzy Normed Spaces ⋮ Nearly quadratic mappings over \(p\)-adic fields ⋮ AMHNMH, AMNM and ADND pairs ⋮ Approximate isomorphisms in \(C^{*}\)-algebras ⋮ Fixed points and functional equations connected with derivations on Banach algebras ⋮ Fixed points and stability of an additive functional equation of \(n\)-Apollonius type in \(C^{\ast}\)-algebras ⋮ Fixed points and Hyers--Ulam--Rassias stability of Cauchy--Jensen functional equations in Banach algebras ⋮ ADDITIVE FUNCTIONAL INEQUALITIES AND DERIVATIONS ON HILBERT C*-MODULES ⋮ Additive functional inequalities in Banach modules ⋮ ON APPROXIMATE n-ARY DERIVATIONS ⋮ Approximately quintic and sextic mappings form \(r\)-divisible groups into Šerstnev probabilistic Banach spaces: fixed point method ⋮ Fixed points and stability of the Cauchy functional equation in \(C^{\ast }\)-algebras ⋮ Stability of the Jensen-type functional equation in \(C^{\ast}\)-algebras: a fixed point approach ⋮ Fuzzy stability of a functional equation associated with inner product spaces ⋮ Solution and stability of an \(n\)-dimensional functional equation ⋮ A converse to Lieb-Robinson bounds in one dimension using index theory ⋮ On the stability of \(J^*\)-homomorphisms ⋮ Approximate \((\alpha ,\beta ,\gamma )\)-derivation on random Lie \(C^*\)-algebras ⋮ Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras

Cites Work

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• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• On the stability of the linear mapping in Banach modules
• Means and convex combinations of unitary operators.
• Approximately Multiplicative Maps Between Banach Algebras
• On the Stability of the Linear Mapping in Banach Spaces

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