Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, the...Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, then the followings are equivalent: 1) (X, T) is a Mazur space; 2) T + (the largest locally convex topology with the same convergent sequence as T) is a compatible topology with T; 3) every sequentially open half-space in (X, T) is open. The relation between Mazur spaces and C-sequential spaces is discussed.展开更多
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 ...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, KSthe （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.展开更多
文摘Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, then the followings are equivalent: 1) (X, T) is a Mazur space; 2) T + (the largest locally convex topology with the same convergent sequence as T) is a compatible topology with T; 3) every sequentially open half-space in (X, T) is open. The relation between Mazur spaces and C-sequential spaces is discussed.
基金Supported by the National Natural Science Foundation of China(10571035,10871141)
文摘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, KSthe （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.
