# Skew product of Hilbert Spaces

I’m researching into relations of Fock spaces (in particular so-called “exponential types”) and in the book Introduction to Algebraic and Constructive Quantum Field Theory by Segal, Baez and Zhou they write that the antisymmitrised Fock space over a direct sum of 2 Hilbert spaces is isomorphic to the “skew product” of the antisymmitrised Fock spaces of both Hilbert spaces.

I’m not familiar with this operation of a skew product, it isn’t defined in the book explictely and I can’t find anything written on it in the context of Hilbert spaces. It carries the symbol of a tensor product symbol with a line underneath, that is: $$H_1 \underline{\otimes } H_2$$ would denote the skew product of two Hilbert spaces $$H_1$$ and $$H_2$$.

Anybody know the definition of this operation?