On Banach spaces containing complemented copies of C0
About certain isomorphic properties of Banach spaces in projective tensor products.
This note is an announcement of results contained in the papers [4], [5], [6] concerning isomorphic properties of Banach spaces in projective tensor products (for this definition and some property we refer to [1]). At the end, some new result is obtained too.
Existence of solutions of a functional-integral equation in infinite dimensional Banach spaces
Existence of solutions of perturbed O.D.E.'s in Banach spaces
We consider a perturbed Cauchy problem like the following and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).
Some permanence results of properties of Banach spaces
Using some known lifting theorems we present three-space property type and permanence results; some of them seem to be new, whereas other are improvements of known facts.
On the position of the space of representable operators in the space of linear operators
We show results about the existence and the nonexistence of a projection from the space of all linear and bounded operators from into onto the subspace of all representable operators.
On complemented copies of in spaces of operators, II
We show that as soon as embeds complementably into the space of all weakly compact operators from to , then it must live either in or in .
Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures
In the paper [5] L. Drewnowski and the author proved that if is a Banach space containing a copy of then is complemented in and conjectured that the same result is true if is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if is a finite measure and is a Banach lattice not containing copies of , then is complemented in . Here, we show that the complementability of in together...
Gelfand-Phillips property in the completion of the space of Pettis integrable functions
Some remarks on the equality
We show that the equality is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product of two Banach spaces under some approximation property type assumptions.
On the Gelfand-Philips Property in ?-tensor Products.
The space of compact operators contains when a noncompact operator is suitably factorized
Uncomplementability of spaces of compact operators in larger spaces of operators
In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results...
An existence theorem for Hammerstein integral equations.
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