As a first step we identify the image of $\Delta$.
Letting $m\to\infty$ identifies this limit as $H$.
Using the standard inner product we can identify $H$ with $H^*$.
The tangent space to $N$ at $x$ is identified with $M$ via left translation.
We henceforth identify $SC(K\times K)$ with a $*$-subalgebra of $L^\infty(X\times X)$.
The resulting metric space consists precisely of the Lebesgue integrable functions, provided we identify any two that are equal almost everywhere.
Go to the list of words starting with: a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
y
z