Banach Journal of Mathematical Analysis

Optimal range theorems for operators with p-th power factorable adjoints

Orlando Galdames Bravo Galdames Bravo and Enrique A. Sanchez Perez

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Consider an operator $T:E \to X(\mu)$ from a Banach space $E$ to a Banach function space $X(\mu)$ over a finite measure $\mu$ such that its dual map is $p$-th power factorable. We compute the optimal range of $T$ that is defined to be the smallest Banach function space such that the range of $T$ lies in it and the restricted operator has $p$-th power factorable adjoint. For the case $p=1$, the requirement on $T$ is just continuity, so our results give in this case the optimal range for a continuous operator. We give examples from classical and harmonic analysis, as convolution operators, Hardy type operators and the Volterra operator.

Article information

Banach J. Math. Anal., Volume 6, Number 1 (2012), 61-73.

First available in Project Euclid: 14 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B38: Operators on function spaces (general)
Secondary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Banach function space, operator vector measure integration optimal range


Galdames Bravo, Orlando Galdames Bravo; Sanchez Perez, Enrique A. Optimal range theorems for operators with p-th power factorable adjoints. Banach J. Math. Anal. 6 (2012), no. 1, 61--73. doi:10.15352/bjma/1337014665.

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