论文标题
正同质对运算符
Orthonormal pairs of operators
论文作者
论文摘要
我们考虑成对的运算符$ a，b \ in B（h）$中，其中$ h $是hilbert空间，因此从$ \ {a，b \} $的跨度中存在线性等距$ f $，in $ \ {a，b \} $ in $ \ mathbb {c}^c}^2 $ mapping $ a，b $ b $ b $ in of OrthononMormal Vectors。我们证明了这种$ F $的存在，并确定通勤正常运营商中的所有这些对。然后，我们表征所有这些对$ a，b $（实际上，我们考虑一般集而不是对成对）的额外要求，即$ f $是完整的等值线，当$ h $带有列（或行）操作员空间结构时。我们还按照与正交范围的c $^*$ - 代数中的元素进行测量表征。
We consider pairs of operators $A,B\in B(H)$, where $H$ is a Hilbert space, such that there exist a linear isometry $f$ from the span of $\{A,B\}$ into $\mathbb{C}^2$ mapping $A,B$ into orthonormal vectors. We prove some necessary conditions for the existence of such an $f$ and determine all such pairs among commuting normal operators. Then we characterize all such pairs $A,B$ (in fact, we consider general sets instead of just pairs) under the additional requirement that $f$ is a complete isometry, when $H$ carries the column (or the row) operator space structure. We also metrically characterize elements in a C$^*$-algebra with orthogonal ranges.
