FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 5, PAGES 153-173

Principles of functional analysis in scales of spaces: Hahn--Banach theorem, Banach theorem on homomorphism, and theorems on open mapping and closed graph

I. V. Orlov

Abstract

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The Hahn--Banach theorem, the Banach theorem on homomorphism, and theorems on open mapping and closed graph are transferred to functionals and operators acting in inductive scales of spaces. The applications to the operators acting in inductive limits and dual spaces are considered.

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Last modified: February 21, 2007