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Tuesday, 12 May 2026 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Nacib Gurgel Albuquerque, Universidade Federal da Paraíba, Brazil<br />
Title: Large Structures and Linear Chaos
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Abstract <br />
<p><span style="color: rgb(0, 0, 0);">This talk explores the interplay between the structural complexity and dynamical behavior of linear operators on infinite-dimensional Fréchet spaces. We first investigate the topology of the space of operators, showing that within the set of non-cyclic operators on a Fréchet space, there exist infinite-dimensional subspaces that are simultaneously dense and closed in the strong operator topology. Focusing on sequence spaces, we further demonstrate that the non-cyclic operators on ℓp (0<p<∞) contain an isometric copy of ℓp itself. Turning to linear dynamics, we analyze unilateral weighted backward shifts on ℓp (1≤p<∞) that support U-frequently hypercyclic subspaces. We prove that such shifts admit U-frequently hypercyclic subspaces that contain no frequently hypercyclic vectors, as well as hypercyclic subspaces that contain no U-frequently hypercyclic vectors, thereby revealing a refined distinction between different notions of frequent hypercyclicity.</span></p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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