Banach Journal of Mathematical Analysis

Extrapolation theorems for (p,q)-factorable operators

Orlando Galdames-Bravo

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The operator ideal of (p,q)-factorable operators can be characterized as the class of operators that factors through the embedding Lq'(μ)Lp(μ) for a finite measure μ, where p,q[1,) are such that 1/p+1/q1. We prove that this operator ideal is included into a Banach operator ideal characterized by means of factorizations through rth and sth power factorable operators, for suitable r,s[1,). Thus, they also factor through a positive map Ls(m1)*Lr(m2), where m1 and m2 are vector measures. We use the properties of the spaces of u-integrable functions with respect to a vector measure and the uth power factorable operators to obtain a characterization of (p,q)-factorable operators and conditions under which a (p,q)-factorable operator is r-summing for r[1,p].

Article information

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

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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]

operator ideal $(p,q)$-factorable operator pth power factorable operator vector measure


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.

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