Pseudo-linearity and linearity (Q1293803)
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scientific article; zbMATH DE number 1310293
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pseudo-linearity and linearity |
scientific article; zbMATH DE number 1310293 |
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Pseudo-linearity and linearity (English)
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29 June 1999
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Concerning the problem, when linearity on the commutative subalgebras implies linearity of a functional on the whole algebra, an example is given of a nonlinear functional on \(M_n(\mathbb{C})\) -- the algebra of complex \(n\times n\)-matrices for an arbitrary \(n\geq 2\) -- but which is linear on each Abelian subalgebra and is bounded on the unit ball.
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pseudo-linearity
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linearity on the commutative subalgebras
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