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This article is cited in 1 scientific paper (total in 1 paper)
On subspace convex-cyclic operators
Jarosław Woźniaka, Dilan Ahmedb, Mudhafar Hamab, Karwan Jwamerb a Institute of Mathematics, Department of Mathematics and Physics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland
b University of Sulaimani, College of Education, Department of Mathematics, Kurdistan Region, Sulaimani, Iraq
Abstract:
Let $\mathcal{H}$ be an infinite dimensional real or complex separable Hilbert space. We introduce a special type of a bounded linear operator $T$ and study its important relation with the invariant subspace problem on $\mathcal{H}$: the operator $T$ is said to be subspace convex-cyclic for a subspace $\mathcal{M}$ if there exists a vector whose orbit under $T$ intersects the subspace $\mathcal{M}$ in a relatively dense set. We give the sufficient condition for a subspace convex-cyclic transitive operator $T$ to be subspace convex-cyclic. We also give a special type of the Kitai criterion related to invariant subspaces which implies subspace convex-cyclicity. Finally we show a counterexample of a subspace convex-cyclic operator which is not subspace convex-cyclic transitive.
Key words and phrases:
ergodic dynamical systems, convex-cyclic operators, Kitai criterion, convex-cyclic transitive operators.
Received: 09.10.2019 Revised: 12.05.2020
Citation:
Jarosław Woźniak, Dilan Ahmed, Mudhafar Hama, Karwan Jwamer, “On subspace convex-cyclic operators”, Zh. Mat. Fiz. Anal. Geom., 16:4 (2020), 473–489
Linking options:
https://www.mathnet.ru/eng/jmag768 https://www.mathnet.ru/eng/jmag/v16/i4/p473
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