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Conical measures and properties of a vector measure determined by its range

L. Rodríguez-Piazza; M. Romero-Moreno — 1997

Studia Mathematica

We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability...

Supercyclicity in the operator algebra

Alfonso Montes-Rodríguez; M. Carmen Romero-Moreno — 2002

Studia Mathematica

We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that certain supercyclic...

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