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Strict Cosingularity and Adjoints for Separable Range

Pełczyński's duality between strictly singular and strictly cosingular operators fails without weak compactness. Beanland asked, in work with Androulakis and later on MathOverflow, for the separable-range case: the paper answers it affirmatively and shows that for separable $X$, $T$ is strictly cosingular exactly when $T^{*}$ is strictly singular.

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analysisJul 19, 2026Significance 10/100Registry: unreviewed

Strict Cosingularity and Adjoints for Separable Range

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Pełczyński's duality between strictly singular and strictly cosingular operators fails without weak compactness. Beanland asked, in work with Androulakis and later on MathOverflow, for the separable-range case: the paper answers it affirmatively and shows that for separable $X$, $T$ is strictly cosingular exactly when $T^{*}$ is strictly singular.

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Pełczyński's duality between strictly singular and strictly cosingular operators fails without weak compactness. Beanland asked, in work with Androulakis and later on MathOverflow, for the separable-range case: the paper answers it affirmatively and shows that for separable $X$, $T$ is strictly cosingular exactly when $T^{*}$ is strictly singular.

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