On the Künneth formula for the reduced cohomology of the tensor product of complexes of Hilbert spaces (Q1963392)

The author studies relations between cohomologies of the tensor product \(K\otimes L\) of two complexes \(K\), \(L\) of Hilbert spaces and cohomologies of factors. In addition, it is shown that the Künneth formula \[ \overline H{}^n(K\otimes L) = \bigoplus_{i+j=n}\overline H{}^i(K)\otimes \overline H{}^j(L) \] holds. The proof is based on the spectral theorem in terms of the product operators.