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On the Balanced Convex Hull of Operator’s Orbit

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Abstract

A bounded linear operator T on a Banach space X is said to be balanced convex-cyclic if the balanced, convex hull generated by orb(T, x) is dense in X for some \(x \in X\). We prove a matrix is balanced convex-cyclic if and only if it is cyclic and all its eigenvalues locate outside of the closed unite disk. Some examples of pure balanced convex-cyclic operators on infinite-dimensional Banach spaces are provided and many properties similar to convex-cyclic operators are considered.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yasouj University, Yasouj, 75914-74831, Iran

    Gh. Baseri, A. I. Kashkooli & H. Rezaei

Authors
  1. Gh. Baseri
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  2. A. I. Kashkooli
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  3. H. Rezaei
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Correspondence to H. Rezaei.

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Baseri, G., Kashkooli, A.I. & Rezaei, H. On the Balanced Convex Hull of Operator’s Orbit. Iran J Sci Technol Trans Sci 46, 659–665 (2022). https://doi.org/10.1007/s40995-022-01274-w

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  • DOI: https://doi.org/10.1007/s40995-022-01274-w

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