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• W2108000743 abstract "Let a, c ≥ 0 and let B be a compact set of scalars. We show that if X is a Banach space such that the canonical projection π from X *** onto X * satisfies the inequality and 1 ≤ λ < max | B | + c , then every λ-commuting bounded compact approximation of the identity of X is shrinking. This generalizes a theorem by Godefroy and Saphar from 1988. As an application, we show that under the conditions described above both X and X * have the metric compact approximation property (MCAP). Relying on the Willis construction, we show that the commuting MCAP does not imply the approximation property." @default.
• W2108000743 created "2016-06-24" @default.
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• W2108000743 date "2009-05-26" @default.
• W2108000743 modified "2023-09-24" @default.
• W2108000743 title "On commuting approximation properties of Banach spaces" @default.
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• W2108000743 doi "https://doi.org/10.1017/s0308210507001266" @default.
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