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Close operator algebras. (English) Zbl 0672.46031
Deformation theory of algebras and structures and applications, Nato Adv. Study Inst., Castelvecchio-Pascoli/Italy 1986, Nato ASI Ser., Ser. C 247, 537-556 (1988).
[For the entire collection see Zbl 0654.00006.]
From the author’s introduction: “The study involves a number of questions such as: Which invariants are stable under a small perturbation of a \(C^*\)-algebra? Are close \(C^*\)-algebras linearly isomorphic? If the algebras are linearly isomorphic through a mapping which is nearly multiplicative, are the algebras then algebraically isomorphic? Is an algebra isomorphism of an algebra A onto an algebra B such that \(\| \phi (a)-a\| \leq \delta \| a\|\) for some small \(\delta\) implemented by an invertible near the identity? The following article presents some positive answers and a pair of counter examples.”
46L05 General theory of \(C^*\)-algebras
46L60 Applications of selfadjoint operator algebras to physics
47A55 Perturbation theory of linear operators