Compact $AC(σ)$ operators

preprint2008arXivOpen access

All compact $AC(σ)$ operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions which allow one to construct a large number of such operators. Using the results in the paper, we answer a number of questions about the decomposition of a compact $AC(σ)$ into real and imaginary parts.

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Compact $AC(σ)$ operators

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Compact $AC(σ)$ operators