# On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces

On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying $$x=\theta _X$$ x = θ X whenever $$p(x)=p(-x)=0$$ p ( x ) = p ( - x ) = 0 . Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a linear space, the theory is different in the asymmetric case. The main purpose of this study is to define bounded and continuous linear operators acting between asymmetric cone normed spaces. After examining the differences with symmetric case, we give some results related to Baire’s characterization of completeness in asymmetric cone normed spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# On The Spaces of Linear Operators Acting Between Asymmetric Cone Normed Spaces

, Volume 15 (3) – May 31, 2018
12 pages

/lp/springer_journal/on-the-spaces-of-linear-operators-acting-between-asymmetric-cone-jkfPUso7a4
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-018-1182-0
Publisher site
See Article on Publisher Site

### Abstract

An asymmetric norm is a positive sublinear functional p on a real vector space X satisfying $$x=\theta _X$$ x = θ X whenever $$p(x)=p(-x)=0$$ p ( x ) = p ( - x ) = 0 . Since the space of all lower semi-continuous linear functionals of an asymmetric normed space is not a linear space, the theory is different in the asymmetric case. The main purpose of this study is to define bounded and continuous linear operators acting between asymmetric cone normed spaces. After examining the differences with symmetric case, we give some results related to Baire’s characterization of completeness in asymmetric cone normed spaces.

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: May 31, 2018

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