Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 2 (2018), 497-514.
Extrapolation theorems for -factorable operators
The operator ideal of -factorable operators can be characterized as the class of operators that factors through the embedding for a finite measure , where are such that . We prove that this operator ideal is included into a Banach operator ideal characterized by means of factorizations through th and th power factorable operators, for suitable . Thus, they also factor through a positive map , where and are vector measures. We use the properties of the spaces of -integrable functions with respect to a vector measure and the th power factorable operators to obtain a characterization of -factorable operators and conditions under which a -factorable operator is -summing for .
Banach J. Math. Anal., Volume 12, Number 2 (2018), 497-514.
Received: 11 July 2017
Accepted: 19 October 2017
First available in Project Euclid: 7 March 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
Secondary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]
Galdames-Bravo, Orlando. Extrapolation theorems for $(p,q)$ -factorable operators. Banach J. Math. Anal. 12 (2018), no. 2, 497--514. doi:10.1215/17358787-2017-0059. https://projecteuclid.org/euclid.bjma/1520413213