Equality of coarse topologies in inverse transformations. (English) Zbl 0893.46020

Burnecki, M.

Acta Univ. Carol., Math. Phys. 37, No. 2, 3-5 (1996).

Summary: In [Indiana Univ. Math. J. 28, 453-469 (1979; Zbl 0401.28017)], J. R. Choksi and S. Kakutani proved that all the strong operator (of course) topologies induced from \({\mathcal L}(L^p(m))\), \(1\leq p<\infty\), coincide on the group of invertible transformations. We show that it holds in a more general setting of Orlicz spaces.

MSC:

46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B28	Spaces of operators; tensor products; approximation properties
28D05	Measure-preserving transformations

Keywords:

strong operator topologies; group of invertible transformations; Orlicz spaces

Citations:

Zbl 0401.28017