Artykuły naukowe (WMiI)

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On the quasi-equivalence of orthogonal bases in non-archimedean metrizable locally convex spaces
(The Belgian Mathematical Society, 2002) Śliwa, Wiesław
We prove that any non-archimedean metrizable locally convex space E with a regular orthogonal basis has the quasi-equivalence property, i.e. any two orthogonal bases in E are quasi-equivalent. In particular, the power series spaces, the most known and important examples of non-archimedean nuclear Frechet spaces, have the quasi-equivalence property. We also show that the Frechet spaces: K^N, c_0xK^N, c_0^N have the quasi-equivalence property.
On the stability of orthogonal bases in non-archimedean metrizable locally convex spaces
(The Belgian Mathematical Society, 2001) Śliwa, Wiesław
It is proved that an orthogonal basis in a non-archimedean metrizable locally convex space E (in particular, a Schauder basis in a non-archimedean Frechet space E) is stable if and only if there is a continuous norm on E. Many others results are also obtained.