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Properties (t) and (gt) for Bounded Linear Operators

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Abstract

In this paper we introduce and study the properties (t) and (gt), which extend properties (w) and (gw). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (t) and property (gt) hold. We also relate these properties with Weyl’s type theorems. We show that if T is a bounded linear operator acting on a Banach space \({\fancyscript{X}}\), then property (gt) holds for T if and only if property (gw) holds for T and σ(T) = σ a (T). Analogously, we show that property (t) holds for T if and only if property (ω) holds for T and σ(T) = σ a (T). We also study the properties (t) and (gt) for the operators satisfying the single valued extension property. Moreover, these properties are also studied in the framework of polaroid operators.

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  1. Department of Mathematics and Statistics, Faculty of Science, Mu’tah University, P.O.Box(7), Al-Karak, Jordan

    M. H. M. Rashid

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  1. M. H. M. Rashid
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Rashid, M.H.M. Properties (t) and (gt) for Bounded Linear Operators. Mediterr. J. Math. 11, 729–744 (2014). https://doi.org/10.1007/s00009-013-0313-x

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  • DOI: https://doi.org/10.1007/s00009-013-0313-x

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