## Banach Journal of Mathematical Analysis

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

#### Abstract

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

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

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1337014665

Digital Object Identifier
doi:10.15352/bjma/1337014665

Mathematical Reviews number (MathSciNet)
MR2862543

Zentralblatt MATH identifier
1276.47003

#### Citation

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. https://projecteuclid.org/euclid.bjma/1337014665