ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46 Ausekle, Jelena, Tartu University, Estonia Compactness of operators acting in the Lorentz and Orlicz Sequence Spaces Let L(X, Y) be the Banach space of all bounded linear operators from X to Y, and let K(X, Y) be the subspace of compact operators. Some versions of the classical Pitt’s theorem (if p > q, then K(ℓ_{p}, ℓ_{q}) = L(ℓ_{p}, ℓ_{q})) for subspaces of Lorentz and Orlicz sequence spaces are established. For example, the following theorem is proved. Let X and Y be closed subspaces of the Lorentz sequence spaces d(v, p) and d(w, q), respectively; if p > q and w ∉ ℓ_{p/(p−q)}, then K(X, Y) = L(X, Y). Part of these results is joint work with E. Oja. Reference: J. Ausekle and E. Oja, Pitt’s theorem for the Lorentz and Orlicz sequence spaces, Mat. Zametki 61 (1997), 18–25 (Russian); English transl. in Math. Notes 61 (1997), 16–21.