论文标题
1型操作员的poset上的星订单自动形态
Star order automorphisms on the poset of type 1 operators
论文作者
论文摘要
令$ \ mathcal {h} $为一个复杂的无限尺寸希尔伯特空间，$ \ Mathcal {b}（\ Mathcal {h}）$ $ \ Mathcal H $上所有有界线性运算符的代数。 $ a \ overset {*} {\ leq} b $定义的星部分订单时，仅当$ a^*a = a^*a = a^*b $和$ aa^*= ab^*= ab^*$用于任何$ a $ a $和$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ b $ in $ \ mathcal b（\ nathcal h）$。我们对恒星顺序进行操作员的类型分解。对于任何$ a \ in \ Mathcal b（\ Mathcal H）$，有独特的1型操作员$ a_1 $，是$ 0 $，或这些等级1运算符的至上少于$ a_1 $和2型操作员$ a_2 $ and $ a_2 $，不超过任何等级1的级别订单中的任何等级1 $ a_i \ a_i \ a_i \ overset $ qued $ qued（$） $ a = a_1+a_2 $。此外，我们确定了1型操作员POSET上的所有自动形态。结果，我们表征了$ \ Mathcal B（\ Mathcal H）$上的连续自动形态。
Let $\mathcal{H}$ be a complex infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal H$. The star partial order is defined by $A\overset{*}{\leq}B$ if and only if $A^*A=A^*B$ and $AA^*=AB^*$ for any $A$ and $B$ in $\mathcal B(\mathcal H)$. We give a type decomposition of operators with respect to star order. For any $A\in\mathcal B(\mathcal H)$, there are unique type 1 operator $A_1 $ which is $0$ or the supremum of those rank 1 operators less than $A_1$ and type 2 operator $A_2$ which is not greater than any rank 1 operator in star order such that $A_i\overset{*}{\leq}A$$(i=1,2)$ and $A=A_1+A_2$. Moreover, we determine all automorphisms on the poset of type 1 operators. As a consequence, we characterize continuous automorphisms on $\mathcal B(\mathcal H)$.
