We study orthogonality preserving and approximately orthogonality preserving mappings in the setting of inner product
C*-modules. In particular, if
V and
W are inner product
C*-modules over the
C*-algebra
![]()
, any scalar multiple of an
![]()
-linear isometry is an
![]()
-linear orthogonality preserving mapping. The converse does not hold in general, but it holds if
![]()
contains
![]()
(the
C*-algebra of all compact operators on a Hilbert space
![]()
). Furthermore, we give the estimate of
![]()
Tx,Ty
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T
2
x,y
32a.gif"" alt=""right-pointing angle bracket"" border=0>![]()
for an
2a36b639"">![]()
-linear approximately orthogonality preserving mapping
T:V→W when
V and
W are inner product
C*-modules over a
C*-algebra containing
![]()
. In the case
![]()
and
V,
W are Hilbert, we also prove that an
![]()
-linear approximately orthogonality preserving mapping can be approximated by an
![]()
-linear orthogonality preserving mapping.