Strongly integrable compact operator families have compact integrals if X has no ell^1, generate countably additive measures if X* has no c0, and satisfy a spectral radius integral inequality for commuting cases.
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Strongly Integrable Operator-Valued Functions, Generated Vector Measures and Compactness of Integrals
Strongly integrable compact operator families have compact integrals if X has no ell^1, generate countably additive measures if X* has no c0, and satisfy a spectral radius integral inequality for commuting cases.