Transitive operator algebras

On topological transitive maps on operator algebras

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.

Strictly Semi-transitive Operator Algebras

An algebra A of operators on a Banach space X is called strictly semitransitive if for all non-zero x, y ∈ X there exists an operator A ∈ A such that Ax = y or Ay = x. We show that if A is norm-closed and strictly semi-transitive, then every A-invariant linear subspace is norm-closed. Moreover, LatA is totally and well ordered by reverse inclusion. If X is complex and A is transitive and strict...

on topological transitive maps on operator algebras

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.

Operator Algebras

Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...

Operator Theory and Operator Algebras