Bounded operators on topological vector spaces and their spectral radii

In this paper, we consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some properties for the spectral radii of a linear operator on a topological vector space. We find some sufficient...

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Bibliographic Details
Published in:Filomat 2012-12, Vol.26 (6), p.1283-1290
Main Authors: Hejazian, Shirin, Mirzavaziri, Madjid, Zabeti, Omid
Format: Article
Language:English
Subjects:
Algebra
Algebraic topology
Continuous spectra
Differential topology
General topology
Linear transformations
Pure mathematics
Topological spaces
Topological vector spaces
Vector spaces
Online Access:Get full text
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Summary:In this paper, we consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some properties for the spectral radii of a linear operator on a topological vector space. We find some sufficient conditions for the completeness of these classes of operators. Finally, as a special application, we deduce some sufficient conditions for invertibility of a bounded linear operator.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1206283H