论文标题
Banach空间中的正交性通过投影张量产品
Orthogonality in Banach Spaces via projective tensor product
论文作者
论文摘要
令$ x $为复杂的Banach空间，$ x，y \ in x $。根据定义，我们说$ x $是birkhoff-james Orthogonal到$ y $，如果$ \ | x+| x+λy\ | _ {x} \ geq \ | x \ | x \ | _ {x} $ for ALL $ c} $ in \ MATHBB {C} $。我们证明，$ x $是birkhoff-james Orthoconal到$ y $，并且仅当存在$ x $上的半米产品$φ$时，因此$ \ |φ\ | | = 1 $，$φ（x，x）= \ | x \ |^2 $和$φ（x，y）= 0 $。类似的结果适用于$ C^*$ - 代数。正交性方法的一个关键点是通过投射张量产品空间的有界双线图的表示。
Let $X$ be a complex Banach space and $x,y\in X$. By definition, we say that $x$ is Birkhoff-James orthogonal to $y$ if $ \|x+λy\|_{X} \geq \|x\|_{X}$ for all $λ\in \mathbb{C}$. We prove that $x$ is Birkhoff-James orthogonal to $y$ if and only if there exists a semi-inner product $φ$ on $X$ such that $\|φ\| = 1$, $φ(x,x)=\|x\|^2$ and $φ(x,y)=0$. A similar result holds for $C^*$-algebras. A key point in our approach to orthogonality is the representations of bounded bilinear maps via projective tensor product spaces.
