Hereditarily transitive tuples

Abstract

In this paper, we characterize conditions under which a tuple of continuous operators is hereditarily transitive. Also, we investigate the relation between hypercyclicity and d-dense orbits of a tuple of operators.

Weighted Composition Operators and Supercyclicity Criterion

“…The vector x is called supercyclic for T if C orb T, x is dense in H. Also a supercyclic operator is one that has a 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] . Let H be a separable Hilbert space of functions analytic on a plane domain G such that, for each λ in G, the linear functional of evaluation at λ given by f → f λ is a bounded linear functional on H. By the Riesz representation theorem, there is a vector K λ in H such that f λ f, K λ .…”

Supercyclicity of Tuples in the Hilbert-Schmidt Operators

“…If X is separable, topologically transitivity of T implies the hypercyclicity of T . For several works see [1][2][3].…”

S-Mixing Tuple of Operators on Banach Spaces

“…This started a new study in the field of hypercyclicity. In [7,8], Yousefi gave the definition of mixing tuples of operators, and he obtained some sufficient conditions for a tuple of continuous operators to be hereditarily transitive and investigated the relationships between hypercyclicity and -dense orbits of a tuple of operators.…”