## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the quasi-equivalence of orthogonal bases in non-archimedean metrizable locally convex spaces

Wiesław Śliwa

#### Abstract

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 $A_1(a)$ and $A_\infty(a)$, the most known and important examples of non-Archimedean nuclear Fréchet spaces, have the quasi-equivalence property. We also show that the Fréchet spaces: ${\Bbb K}^{\Bbb N},c_0\times{\Bbb K}^{\Bbb N},c^{\Bbb N}_0$ have the quasi-equivalence property.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 9, Number 3 (2002), 465-472.

Dates
First available in Project Euclid: 1 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1298991753

Digital Object Identifier
doi:10.36045/bbms/1298991753

Mathematical Reviews number (MathSciNet)
MR2016585

Zentralblatt MATH identifier
1039.46054

#### Citation

Śliwa, Wiesław. On the quasi-equivalence of orthogonal bases in non-archimedean metrizable locally convex spaces. Bull. Belg. Math. Soc. Simon Stevin 9 (2002), no. 3, 465--472. doi:10.36045/bbms/1298991753. https://projecteuclid.org/euclid.bbms/1298991753