Open Access
may 2014 Generalized Kӧthe $p$-dual spaces
O. Galdames Bravo
Bull. Belg. Math. Soc. Simon Stevin 21(2): 275-289 (may 2014). DOI: 10.36045/bbms/1400592625


Let us consider a Banach function space $X$. The Kӧthe dual space can be characterized as the space of multipliers from $X$ to $L^1$. We extend this characterization to the space of multipliers from $X$ to $L^p$ in order to define the Kӧthe $p$-dual space of $X$. We analyze the properties of this space so as to use it as a tool for studying $p$-th power factorable operators. In particular, we compute $q$-concavity for these spaces and type and cotype when $X$ is an AM-space. As main applications, we give a characterization for Hilbert Banach function spaces, as well as a factorization for $p$-th power factorable operators through an $L^{p,\infty}$-space.


Download Citation

O. Galdames Bravo. "Generalized Kӧthe $p$-dual spaces." Bull. Belg. Math. Soc. Simon Stevin 21 (2) 275 - 289, may 2014.


Published: may 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1308.46038
MathSciNet: MR3211016
Digital Object Identifier: 10.36045/bbms/1400592625

Primary: 46A20
Secondary: 32F10 , 46B20

Keywords: $p$-concavity , Banach function space , cotype , Kӧthe dual space , space of multipliers , type

Rights: Copyright © 2014 The Belgian Mathematical Society

Vol.21 • No. 2 • may 2014
Back to Top