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The problem of S. M. Ulam for approximately multiplicative mappings. (English) Zbl 0958.46022

The author discusses the celebrated Ulam’s problem of describing the functionals satisfying an \(\varepsilon\)-version of multplicative or additive law. The structure of a so-called ANMN-algebra, i.e., an algebra with “integrity”, that is, whose every approximately miltiplicative functional is near multiplicative.

MSC:

46G05 Derivatives of functions in infinite-dimensional spaces
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