The name for the the following 2 mathematical objects:

• $$H_2(G,\mathbb{Z})$$ and

• $$\{K:G\times G\longrightarrow\mathbb{C}\ |\ \forall T\in B(l^2(G))\ we\ have\ that\ S:G\times G\longrightarrow\mathbb{C}\ defined\ by\ \\ S(g,h)=K(g,h)T(g,h)\ also\ represents\ an\ element\ of\ B(l^2(G))\}$$ where $T$ and $S$ are seen as infinite matrices in the the canonical basis of $l^2(G)$

is the same: Schur multiplier of a group. Why? Is there a strong connection between them? I'd say it comes from the fact that originally $H_2(G,\mathbb{Z})$ was defined as $H^2(G,\mathbb{C}^*)$ which has to do with projective representations, and representations are related to the second object. But infinite groups interest me more.

I think Herz first defined and gave the name to the second object, but I don't know why he chose this name which already exited in the literature, unless there is a strong link between them. (the paper is in French and I can't read it).