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

• D. Puglisi, J.B. Seoane-Sepulveda; Bounded linear non-absolutely summing operators J. Math. Anal. Appl. 338 (2008), 292-298.

amoung other things, the authors show that if F is a Banach space and E is a Banach space with the two series property (i.e., sufficiently Euclidean Banach space), then the set of bounded linear and non-absolutely summing operators from E to F* is lineable.

Questions

• Let E is superreflexive and F is any Banach space. Is the set of bounded linear and non-absolutely p-summing operators from E to F lineable?
• Let E be a Banach space with the approximation property but failing the bounded approximation property, such that E* separable. Is the set of non-nuclear operators (and with nuclear adjoint) on E lineable?

Comments

• D. Kitson, R.M. Timoney; Operator ranges and spaceability. J. Math. Anal. Appl. 378 (2011), no. 2, 680–686.

The first question was motivated by

• W.J. Davis, W.B. Johnson, Compact, non-nuclear operators, Studia Math. 51 (1974) 81–85.

• T. Figiel, W.B. Johnson, The approximation property does not imply the bounded approximation property, Proc. Amer. Math. Soc. 41 (1973) 197–200.

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