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Discontinuity of the product in multiplier algebras.

Mohamed Oudadess (1990)

Publicacions Matemàtiques

Entire functions operate in complete locally A-convex algebras but not continuously. Actually squaring is not always continuous. The counterexample we give is multiplier algebra.

Nonassociative real H*-algebras.

Miguel Cabrera, José Martínez Aroza, Angel Rodríguez Palacios (1988)

Publicacions Matemàtiques

We prove that, if A denotes a topologically simple real (non-associative) H*-algebra, then either A is a topologically simple complex H*-algebra regarded as real H*-algebra or there is a topologically simple complex H*-algebra B with *-involution τ such that A = {b ∈ B : τ(b) = b*}. Using this, we obtain our main result, namely: (algebraically) isomorphic topologically simple real H*-algebras are actually *-isometrically isomorphic.

Nonlinear * -Lie higher derivations of standard operator algebras

Mohammad Ashraf, Shakir Ali, Bilal Ahmad Wani (2018)

Communications in Mathematics

Let be an infinite-dimensional complex Hilbert space and 𝔄  be a standard operator algebra on which is closed under the adjoint operation. It is shown that every nonlinear * -Lie higher derivation 𝒟 = { δ n } n of 𝔄 is automatically an additive higher derivation on 𝔄 . Moreover, 𝒟 = { δ n } n is an inner * -higher derivation.

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