Let
V
V
denote an infinite dimensional Banach space over the complex field,
B
[
V
]
B[V]
the bounded linear operators on
V
V
and
F
F
a closed subspace of
V
V
. An element of
T
F
=
{
T
|
T
∈
B
[
V
]
,
T
(
F
)
⊆
F
}
{\mathcal {T}_F} = \{ T|T \in B[V],T(F) \subseteq F\}
is called a conservative operator. Some sufficient conditions for
T
∈
T
F
T \in {\mathcal {T}_F}
to be in the boundary,
B
\mathcal {B}
, of the maximal group,
M
\mathcal {M}
, of invertible elements are determined. For example, if
T
∈
T
F
T \in {\mathcal {T}_F}
, is such that (i)
V
V
is the topological direct sum of
R
(
T
)
\mathcal {R}(T)
and
N
(
T
)
≠
{
θ
}
N(T) \ne \{ \theta \}
, (ii)
T
T
is an automorphism on
R
(
T
)
∩
F
\mathcal {R}(T) \cap F
, then
T
∈
B
T \in \mathcal {B}
. Also, the complement of the closure of
M
\mathcal {M}
is discussed. This is an extension of another paper by the same authors [6].