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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2026 2verdicts
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Generalizes Gel'fand integration of B(E,F*)-valued functions to Banach spaces, gives conditions for the integral to be (q,p)-summing, and answers an open question from prior work.
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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.
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Gel'fand Integration of B(E, F*)-Valued Functions With Emphasis on (q, p)-Summing Operators
Generalizes Gel'fand integration of B(E,F*)-valued functions to Banach spaces, gives conditions for the integral to be (q,p)-summing, and answers an open question from prior work.