GoI for MELL: exponentials
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The tensor product of Hilbert spaces</math>
Recall that is the canonical basis of . The space is the collection of sequences of complex numbers such that:
∑ | | x_{np} | ^{2} |
n,p |
converges. The scalar product is defined just as before:
- .
The canonical basis of is denoted where e_{ij} is the (doubly indexed) sequence defined by:
- e_{ijnp} = δ_{in}δ_{jp} (all terms are null but the one at index (i,j) which is 1).
If and are vectors in H then their tensor is the sequence:
- .
In particular we have: and we can write: