Hypercyclicity on the Algebra of Hilbert-Schmidt Operators

Yousefi, B.; Rezaei, Hamid

doi:10.1007/bf03322879

Cited by 19 publications

(9 citation statements)

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“…Study of hypercyclicity in operator algebras was initiated by Chan to construct hypercyclic subspaces [5], and his idea was subsequently used by several authors, see [3,6,15,18]. Indeed, the concept of SOT-hypercyclicity of L T was studied in [5] for operators on Hilbert spaces.…”

Section: Introductionmentioning

confidence: 99%

Supercyclicity in Spaces of Operators

Gupta

Mundayadan

2015

Results. Math.

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A sufficient criterion for the map CA,B(S) = ASB to be supercyclic on certain algebras of operators on Banach spaces is given. If T is an operator satisfying the Supercyclicity Criterion on a Hilbert space H, then the linear map CT (V ) = T V T * is shown to be norm-supercyclic on the algebra K(H) of all compact operators, COT-supercyclic on the real subspace S(H) of all self-adjoint operators and weak * -supercyclic on L(H) of all bounded operators on H. Examples including operators of the form CB w ,Fμ are provided, where Bw and Fµ are respectively backward and forward shifts on Banach sequence spaces. Mathematics Subject Classification. Primary 47A16; Secondary 47L05.

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Section: Introductionmentioning

confidence: 99%

Supercyclicity in Spaces of Operators

Gupta

Mundayadan

2015

Results. Math.

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“…A tuple of operators is ǫ-supercyclic if it admits an ǫ-supercyclic vector. For some sources on these topics see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Tuple of Operators and Epsilon Supercyclicity

Yousefi¹,

Izadi²

2014

Int. J. of Pure and Appl. Math.

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“…Here, we want to extend some properties of hypercyclic operators to a pair of commuting operators, and although the techniques work for any n-tuple of operators but for simplicity we prove our results only for the case n = 2. For some other topics we refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%