154 research outputs found
Duality in spaces of finite linear combinations of atoms
In this note we describe the dual and the completion of the space of finite
linear combinations of -atoms, on . As
an application, we show an extension result for operators uniformly bounded on
-atoms, , whose analogue for is known to be false.
Let and let be a linear operator defined on the space of finite
linear combinations of -atoms, , which takes values in a
Banach space . If is uniformly bounded on -atoms, then
extends to a bounded operator from into .Comment: The paper has appeared as Ricci, F., & Verdera, J. (2011). Duality in
spaces of finite linear combinations of atoms. Transactions of the American
Mathematical Society, 363(3), 1311-132
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