Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inner products and module maps of Hilbert C*-modules   Let $E$ and $F$ be two Hilbert $C^*$-modules over $C^*$-algebras $A$ and $B$,
respectively. Let $T$ be a surjective linear isometry from $E$ onto $F$ and
$\varphi$ a map from $A$ into $B$. We will prove in this paper that if the
$C^*$-algebras $A$ and $B$ are commutative, then $T$ preserves the inner
products and $T$ is a module map, i.e., there exists a $*$-isomorphism
$\varphi$ between the $C^*$-algebras such that $$ \langle
Tx,Ty\rangle=\varphi(\langle x,y\rangle), $$ and $$ T(xa)=T(x)\varphi(a). $$ In
case $A$ or $B$ is noncommutative $C^*$-algebra, $T$ may not satisfy the
equations above in general. We will also give some condition such that $T$
preserves the inner products and $T$ is a module map.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg