Advances in Operator Theory

Topological properties of operations on spaces of differentiable functions

Fernanda Botelho and Holly Renaud

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‎‎In this paper‎, ‎we consider different notions of openness for the scalar multiplication on sequence spaces and spaces of continuous functions‎. ‎We apply existing techniques to derive weak openness of multiplication on spaces of differentiable functions‎, ‎endowed with a large collection of quasi-algebra norms‎.

Article information

Adv. Oper. Theory, Volume 4, Number 1 (2019), 305-320.

Received: 24 April 2018
Accepted: 24 September 2018
First available in Project Euclid: 29 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

open map weak openness ‎dense openness‎‎‎ ‎space of continuously differentiable functions


Botelho, Fernanda; Renaud, Holly. Topological properties of operations on spaces of differentiable functions. Adv. Oper. Theory 4 (2019), no. 1, 305--320. doi:10.15352/aot.1804-1351.

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