we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

in this paper, by presenting some notions and theorems, we obtaindifferent types of fuzzy topologies. in fact, we obtain somelowen-type  and chang-type fuzzy topologies on general fuzzyautomata. to this end, first we define a kuratowski fuzzy interioroperator which induces a  lowen-type  fuzzy topology on the  set ofstates of a max- min general   fuzzy automaton. also by  provingsome theorems, ...

We prove that if {φt}t≥0 is a CP-semigroup acting on a von Neumann algebra M ⊆ B(H), then for every A ∈ M and ξ ∈ H , the map t 7→ φt(A)ξ is norm-continuous. We discuss the implications of this fact to the existence of dilations of CPsemigroups to semigroups of endomorphisms.