Daniele Puglisi

Department of Mathematics and Computer Sciences
University of Catania
Viale Andrea Doria, 6
I-95125 Catania CT

Office: 346
Office phone: ++39 095 7383055
Fax: ++39 095 330094

E-mail: dpuglisiunict.it

Research

In

• L. Janicka, N. Kalton, Vector measures of infinite variation, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (3) (1977) 239–241.

throughout porbabilistic methods, it is proved that if X is an infinite dimensional Banach space then there exists a non-trivial X-valued measure with relatively compact range such that its variation measure assumes the value infinity on every non-null set. In

• G. A. Munoz-Fernandez, N. Palmberg, D. Puglisi, J. B. Seoane- Sepulveda; Lineability in subsets of measure and function spaces. Linear Algebra Appl. 428 (2008), 2805-2812.

using a direct construction, it is proved that the set of \ell_p-valued measures with relatively compact range and such that their variation measure takes the value infinity on every non-null set is lineable.

Also, related to the classical Liapounov theorem, the authors proved that if \lambda be the Lebesgue measure on the Borel sets in [0, 1], and X be an infinite dimensional Banach space, then the set of measures whose range is neither closed nor convex is lineable in ca(\lambda,X)

Questions

• Is the set of X-valued measures with relatively compact range and such that their variation measure takes the value infinity on every non-null set, for a infinite dimensional Banach space X, lineable?
• What about spaceability?
• Let X be an infinite dimensional Banach space. Is the set of measures whose range is neither closed nor convex is spaceable in ca(\lambda,X)?

Comments

• G. Barbieri, F.J. Garcia-Pacheco, D. Puglisi; Lineability and spaceability on vector-measure spaces. preprint (2013)

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