Noncommutative point derivations for matrix function algebras

Details Noncommutative point derivations for matrix function algebras Noncommutative point derivations for matrix function algebras

2005-03-28

arxiv.org/abs/math/0503643v4

Linear Algebra and Its Applications 422 (2007), 67-76

Mathematics

Operator Algebras

11 pages, this version (3rd version) updates some notation and corrects typographical errors

Scientific paper

We study a class of matrix function algebras, here denoted $\mathcal{T}^{+}(\mathcal{C}_n)$. We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of $\mathcal{T}^{+}(\mathcal{C}_n)$. We use point derivations and information about $n \times n$ matrices to show that every $\mathcal{T}^{+}(\mathcal{C}_n)$-valued derivation on $\mathcal{T}^{+}(\mathcal{C}_n)$ is inner.

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