In this paper,we characterize conditions under which a tuple of bounded linear operators is topologically mixing.Also,we give conditions for a tuple to be hereditarily hypercyclic with respect to a tuple of syndetic sequences. 相似文献
Let X denote a specific space of the class of Xα,p Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily ℓp Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of ℓp. It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of ℓp where 1/p + 1/q = 1. For p = 1 it is known that the predual of the Banach space X contains asymptotically isometric copies of c0. Here we give a direct proof of the known result that X contains asymptotically isometric copies of ℓ1. 相似文献
We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators on separable complex -spaces: is frequently hypercyclic if there exists a vector such that for every nonempty open subset of , the set of integers such that belongs to has positive lower density. We give several criteria for frequent hypercyclicity, and this leads us in particular to study linear transformations from the point of view of ergodic theory. Several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting.
Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, Köthe (LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems. 相似文献
In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly -to-1 image of any continuum if . Since that time, no other class of continua has been shown to have this same property. It is shown that no hereditarily indecomposable tree-like continuum is the continuous, exactly -to-1 image of any continuum if .
In this paper we prove that the product of a Baire space with a metrizable hereditarily Baire space is again a Baire space. This answers a recent question of J. Chaber and R. Pol.
The present paper shows that the algebra
generated by {C| Aut(Bn)} is cyclic on H2(Bn), and any nonconstant function fH2(Bn) is a cyclic vector of
. In addition, the hypercyclic and cyclic composition operators will be discussed. 相似文献
Every Banach space either contains a subspace isomorphic to , or it has an infinite-dimensional closed subspace which is a quotient of a Hereditarily Indecomposable (H.I.) separable Banach space.
In the particular case of , it is shown that the space itself is a quotient of a H.I. space. The factorization of certain classes of operators, acting between Banach spaces, through H.I. spaces is also investigated. Among others it is shown that the identity operator admits a factorization through a H.I. space. The same result holds for every strictly singular operator .
Interpolation methods and the geometric concept of thin convex sets together with the techniques concerning the construction of Hereditarily Indecomposable spaces are used to obtain the above mentioned results. 相似文献
We deal with the problem asking whether hereditarily finite superstructures have elementary extensions of the form
. In so doing, we settle the question whether a theory for some hereditarily finite superstructure have
models of arbitrarily large cardinality. A Hanf number is shown to exist, and we provide an exact bound for the countable case. 相似文献