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Explore Stack InternalSay $A$ and $B$ are operators on Hilbert spaces $H_A,H_B$ respectively. If the Hilbert spaces are finite dimensional, then I know the tensor $A\otimes B$ can be represented by the Kronecker product $[a_{ij}B]$.
Question 1: Does the Kronecker product formula $[a_{ij}B]$ still work in infinite dimensions?
Question 2: If not, does it work when $A$$H_A$ is finite dimension and $B$$H_B$ is infinite dimensional (possibly an operator on a non-separable space)?
Say $A$ and $B$ are operators on Hilbert spaces respectively. If the Hilbert spaces are finite dimensional, then I know the tensor $A\otimes B$ can be represented by the Kronecker product $[a_{ij}B]$.
Question 1: Does the Kronecker product formula $[a_{ij}B]$ still work in infinite dimensions?
Question 2: If not, does it work when $A$ is finite dimension and $B$ is infinite dimensional (possibly an operator on a non-separable space)?
Say $A$ and $B$ are operators on Hilbert spaces $H_A,H_B$ respectively. If the Hilbert spaces are finite dimensional, then I know the tensor $A\otimes B$ can be represented by the Kronecker product $[a_{ij}B]$.
Question 1: Does the Kronecker product formula $[a_{ij}B]$ still work in infinite dimensions?
Question 2: If not, does it work when $H_A$ is finite dimension and $H_B$ is infinite dimensional (possibly an operator on a non-separable space)?
Say $A$ and $B$ are operators on Hilbert spaces respectively. If the Hilbert spaces are finite dimensional, then I know the tensor $A\otimes B$ can be represented by the Kronecker product $[a_{ij}B]$.
Question 1: Does the Kronecker product formula $[a_{ij}B]$ still work in infinite dimensions?
Question 2: If not, does it work when $A$ is finite dimension and $B$ is infinite dimensional (possibly an operator on a non-separable space)?
