Results 1 to 10 of about 52 (46)

About subspace-frequently hypercyclic operators [PDF]

Sahand Communications in Mathematical Analysis, 2020
Summary: In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic operators that are not subspace-frequently hypercyclic. There is a criterion like the subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator \
Moosapoor, Mansooreh, Shahriari, Mohammad   +1 more
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Subspace-hypercyclic weighted shifts [PDF]

Operators and Matrices, 2018
Our aim in this paper is to obtain necessary and sufficient conditions for weighted shift operators on the Hilbert spaces $\ell^{2}(\mathbb Z)$ and $\ell^{2}(\mathbb N)$ to be subspace-transitive, consequently, we show that the Herrero question (D. A. Herrero. Limits of hypercyclic and supercyclic operators, J. Funct.
Bamerni, Nareen, Kiliçman, Adem
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On subspace-diskcyclicity

Arab Journal of Mathematical Sciences, 2017
In this paper, we define and study subspace-diskcyclic operators. We show that subspace-diskcyclicity does not imply diskcyclicity. We establish a subspace-diskcyclic criterion and use it to find a subspace-diskcyclic operator that is not subspace ...
Nareen Bamerni, Adem Kılıçman
doaj   +1 more source

Subspace hypercyclicity

Journal of Mathematical Analysis and Applications, 2011
15 ...
Madore, Blair F., Martínez-Avendaño, Rubén A.   +1 more
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Hypercyclic operators are subspace hypercyclic

Journal of Mathematical Analysis and Applications, 2016
A bounded operator \(T\) on a separable Banach space \(X\) is called subspace hypercyclic for a subspace \(M\) of \(X\) if there is a vector \(x \in X\) such that the intersection of its orbit and \(M\) is dense in \(M\). The aim of this paper is to solve a question of \textit{B. F. Madore} and \textit{R. A. Martínez-Avendaño} [J. Math. Anal. Appl. 373,
Nareen Bamerni, Vladimir Kadets, Adem Kılıçman   +2 more
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Spectral theory and hypercyclic subspaces [PDF]

Transactions of the American Mathematical Society, 2000
Let \(T\) be a bounded linear operator in a Hilbert space \(H\). A vector \(x\) in \(H\) is called hypercyclic for \(T\) if its orbit \((T^n x : n > 0)\) is dence in \(H\). The main results of the authors reads as follows: If \(T\) satisfy the hypercyclicty criterion of C.
León-Saavedra, Fernando, Montes-Rodríguez, Alfonso   +1 more
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Hereditarily hypercyclic subspaces [PDF]

Journal of Operator Theory, 2015
We say that a sequence of operators $(T_n)$ possesses hereditarily hypercyclic subspaces along a sequence $(n_k)$ if for any subsequence $(m_k)\subset(n_k)$, the sequence $(T_{m_k})$ possesses a hypercyclic subspace. While so far no characterization of the existence of hypercyclic subspaces in the case of Fr chet spaces is known, we succeed to obtain ...
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Hypercyclic subspaces in omega

Journal of Mathematical Analysis and Applications, 2006
A continuous linear operator \(T\) acting on a Fréchet space \(X\) is called hypercyclic if there exists a vector \(x\in X\) whose orbit Orb\((T,x)=\{x, T(x), T^2(x), \ldots\}\) is dense in \(X\). Such a vector \(x\) is called a hypercyclic vector for \(T\). A hypercyclic manifold for \(T\) is a dense, invariant subspace of \(X\) consisting entirely --
Bès, Juan, Conejero, José A.
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On subspace-hypercyclic operators [PDF]

Proceedings of the American Mathematical Society, 2011
In this paper we study an operator T T on a Banach space E E which is M M -hypercyclic for some subspace M M of E E . We give a sufficient condition for such an operator to be M M -hypercyclic and use it to answer negatively two questions asked by ...
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HYPERCYCLICITY ON INVARIANT SUBSPACES [PDF]

Journal of the Korean Mathematical Society, 2008
A continuous linear operator T : X -> X is called hypercyclic if there exists an x is an element of X such that the orbit {T(n)x}(n >= 0) is dense. We consider the problem: given an operator T : X -> X, hypercylic or not, is the restriction T vertical bar y to some closed invariant subspace Y subset of X hypercyclic?
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