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[parent] example of Banach algebra which is not a $C^*$-algebra for any involution (Example)
ExampleOfBanachAlgebraWhichIsNotACAlgebraForAnyInvolution

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Also defines:  finite dimensional $C^*$-algebras are semi-simple

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Cross-references: matrix, diagonal, maximal ideal, easy to see, nilpotent, algebra, ideal, element, Jacobson radical, semi-simple, theorem, finite dimensional, proof, involution, identity matrix, matrix norm, matrix operations, Banach algebra

This is version 2 of example of Banach algebra which is not a $C^*$-algebra for any involution, born on 2007-07-28, modified 2007-08-17.
Object id is 9807, canonical name is ExampleOfBanachAlgebraWhichIsNotACAlgebraForAnyInvolution.
Accessed 1342 times total.

Classification:
AMS MSC46L05 (Functional analysis :: Selfadjoint operator algebras :: General theory of $C^*$-algebras)

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