论文标题
Banach $ \ star $ -Algebras上的连续双线性地图
Continuous bilinear maps on Banach $\star$-algebras
论文作者
论文摘要
让$ a $是Unital Banach $ \ star $ -Algebra，unity $ 1 $，$ x $是Banach空间，$ ϕ：A \ times a \ to x $是连续的双线性图。我们表征了$ ϕ $的结构，其中满足以下任何属性：$$ a，b \ in a，\，\，\，a b^\ star = z \，\，（a^\ star b = z）\ rightArolOw ϕ（a，b^\ star）=（a，b^\ star）= ϕ（z，1）\ s） $ a，b \在a，\，\，\中，a b^\ star = z \，\，（a^\ star b = z）\ rightarrow ϕ（a，b^\ star）= ϕ（1，z）\，\，\，（ϕ（ϕ（A^\ star，b）=（a^\ star，b）= ϕ（1，z）$ z questect
Let $A$ be a unital Banach $\star$-algebra with unity $1$, $X$ be a Banach space and $ϕ: A \times A \to X$ be a continuous bilinear map. We characterize the structure of $ϕ$ where it satisfies any of the following properties: $$a,b \in A, \,\,\, a b^\star = z \, \,(a^\star b=z)\Rightarrow ϕ( a , b^\star ) = ϕ( z, 1 ) \, \, (ϕ( a^\star , b) = ϕ( z, 1 ));$$ $$a,b \in A, \,\,\, a b^\star = z \, \, (a^\star b=z)\Rightarrow ϕ( a , b^\star ) = ϕ( 1, z ) \, \, (ϕ( a^\star , b) = ϕ( 1, z )),$$ where $z\in A$ is fixed.
