Absolutely (r, q)-Summing Operators on Vector-Valued Function Spaces

作者：Munoz Fernando^*; Oja Eve; Pineiro Candido

来源：Integral Equations and Operator Theory, 2017, 89(1): 69-88.

DOI：10.1007/s00020-017-2376-8

• Banach spaces
• Absolutely (r, q)- and absolutely p-summing operators
• Operator-valued measures
• p-Continuous vector-valued functions
• r-Variation

Let X and Y be Banach spaces and let be a compact Hausdorff space. In 1973, Swartz, in his by now classical theorem, characterized the absolute summability of an operator U from to Y in terms of its associated operator and of its representing measure m. We study the interplay between U, , and m in the context of absolutely (r, q)-summing operators, considering the spaces of p-continuous functions on , , instead of . This encompasses the Swartz theorem together with its existing extensions on absolutely (r, q)-summing operators, providing, among others, an improvement even to the Swartz theorem. Counterexamples are exhibited to indicate sharpness of our results.

• 出版日期2017-9