算子空间上的左乘映射

Let X be a separable infinite dimensional Banach space and B(X) denote its operator algebra,the algebra of all bounded linear operators T : X → X.Define a left multiplication mapping LT : B(X) → B(X) by LT (V ) = T V,V ∈ B(X).We investigate the connections between hypercyclic and chaotic behaviors of the left multiplication mapping LT on B(X) and that of operator T on X.We obtain that LT is SOT-hypercyclic if and only if T satisfies the Hypercyclicity Criterion.If we define chaos on B(X) as SOT-hypercyclicity plus SOT-dense subset of periodic points,we also get that LT is chaotic if and only if T is chaotic in the sense of Devaney.

Left Multiplication Mappings on Operator Spaces

Let $X$ be a separable infinite dimensional Banach space and $B(X)$ denote its operator algebra, the algebra of all bounded linear operators $T: Xrightarrow X$. Define a left multiplication mapping $L_T: B(X)rightarrow B(X)$ by $L_T(V)=TV,~ V in B(X)$. We investigate the connections between hypercyclic and chaotic behaviors of the left multiplication mapping $L_T$ on $B(X)$ and that of operator $T$ on $X$. We obtain that $L_T$ is SOT-hypercyclic if and only if $T$ satisfies the Hypercyclicity Criterion. If we define chaos on $B(X)$ as SOT-hypercyclicity plus SOT-dense subset of periodic points, we also get that $L_T$ is chaotic if and only if $T$ is chaotic in the sense of Devaney.