Bounded operators on topological vector spaces and their spectral radii | Zendy

Shirin Hejazian | Zendy; Madjid Mirzavaziri | Zendy; Omid Zabeti | Zendy

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Bounded operators on topological vector spaces and their spectral radii

Author(s) -

Shirin Hejazian,

Madjid Mirzavaziri,

Omid Zabeti

Publication year - 2012

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1206283h

Subject(s) - mathematics , bounded function , topological vector space , bounded operator , completeness (order theory) , continuous linear operator , spectral radius , linear operators , operator (biology) , topology (electrical circuits) , finite rank operator , operator theory , topological space , space (punctuation) , operator norm , pure mathematics , mathematical analysis , banach space , eigenvalues and eigenvectors , combinatorics , computer science , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , gene , operating system

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.

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