equal
deleted
inserted
replaced
2420 \[ |
2420 \[ |
2421 z_Y : \cS(Y\cup\ol{Y}) \to \c. |
2421 z_Y : \cS(Y\cup\ol{Y}) \to \c. |
2422 \] |
2422 \] |
2423 We will also use the notation |
2423 We will also use the notation |
2424 \[ |
2424 \[ |
2425 \langle a, b\rangle \deq z_Y(a\bullet \ol{b}) \in \c . |
2425 \langle a, b\rangle \deq z_Y(a\bullet b) \in \c . |
2426 \] |
2426 \] |
2427 An inner product induces a linear map |
2427 An inner product induces a linear map |
2428 \begin{eqnarray*} |
2428 \begin{eqnarray*} |
2429 \varphi: \cS(Y) &\to& \cS(Y)^* \\ |
2429 \varphi: \cS(Y) &\to& \cS(Y)^* \\ |
2430 a &\mapsto& \langle a, \cdot \rangle |
2430 a &\mapsto& \langle a, \cdot \rangle |