A new spectral properties for linear operators in Banach space

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A new spectral properties for linear operators in Banach space

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Abstract

The main results of these studies consisted in finding new spectral properties of as bounded linear operators $T $ and $S$ defined on a Banach space, such as $TST=T^2\sqrt{T}$ and $STS=S^2 \sqrt{S}$. The novelty of this work is to extend the study of Christoph Schmoeger {\cite{6ch}} where the spectral properties of two operators $T $ and $S$ given as $TST=T^2$ and $ STS= S^2 $ were addressed and \cite{Anuradha} in which the operators are taken $T^\tau S^kT^\tau=T^{\tau+1}$ and $S^\tau T^\tau S^\tau=S^{\tau+1}$, $\tau$ is a positive integer . These two works will be a special case of our results.

Keywords

Common spectral properties Mathematical Operators Drazin invertibility Operator equation Sequence Analysi Mathematical model.

References

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