A. E. Gutman, S. A. Lisovskaya, “The boundedness principle for lattice-normed spaces”, Sibirsk. Mat. Zh., 2009, Volume 50, Number 5,Pages <nobr>1050

This article is cited in 4 papers

The boundedness principle for lattice-normed spaces

A. E. Gutman^a, S. A. Lisovskaya^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk

Abstract: The three classical facts of the theory of normed spaces are considered: the boundedness principle, the Banach–Steinhaus theorem, and the uniform boundedness principle for a compact convex set. By means of Boolean valued analysis, the analogs of the theorems are proven in a lattice-normed space setting.

Keywords: Banach–Steinhaus theorem, Banach–Kantorovich space, cyclically compact set, Boolean valued analysis.

UDC: 517.98

Received: 02.06.2009