Atlas: On copies of c_0 in the bounded linear operator space by Jose M. Amigo

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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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On copies of c_0 in the bounded linear operator space
by
José M. Amigó
Universidad Miguel Hernández
Coauthors: J.C. Ferrando (Universidad Miguel Hernández)

Since the Bessaga and Pelczynski seminal result on the characterization of Banach spaces containing c₀ (the Banach space of null sequences), the properties of normed spaces having (eventually complemented) copies of certain classical Banach spaces of sequences (c₀, l₁, ...) have been studied by many authors (Bonet et al., Cembranos and Mendoza, Drewnowski, Emmanuelle, Ferrando, Kalton, Rosenthal, ...). Typically, one considers some normed space F(X, Y) of functions from a normed space X into a Banach space Y and studies the interplay between X or Y having a (complemented) copy of, say, c₀ and F(X, Y) having a (complemented) copy of c₀ or some other Banach sequence space.

The particular case when the function space considered is L(X, Y), the Banach space of bounded linear operators provided with the operator norm, will be addressed in this talk. Applying a general technique which also works in other settings, one deduces the existence of copies of c₀ in Y under different hypotheses on L(X, Y). These results can be extended to the space of all bounded vector measures. Some ''dual'' results, such as the existence of a copy of l_\infty in L(Y^*, l₁) if X contains a copy of c₀, follow as well.

(T)

Date received: April 18, 2000