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Um subconjunto
S
{\displaystyle S\,\!}
espaço vectorial
X
{\displaystyle X\,\!}
corpo
K
{\displaystyle \mathbb {K} }
equilibrado se, para qualquer elemento
x
{\displaystyle x\,\!}
S
{\displaystyle S\,\!}
λ
∈
K
{\displaystyle \lambda \in \mathbb {K} }
|
λ
|
≤
1
{\displaystyle |\lambda |\leq 1}
λ
x
∈
S
{\displaystyle \lambda x\in S}
Qualquer subespaço vectorial de
X
{\displaystyle X}
Se
(
S
i
)
i
∈
I
{\displaystyle (S_{i})_{i\in I}}
X
{\displaystyle X\,\!}
⋂
i
∈
I
S
i
{\displaystyle \bigcap \limits _{i\in I}S_{i}}
Se
(
S
n
)
n
∈
N
{\displaystyle (S_{n})_{n\in \mathbb {N} }}
X
{\displaystyle X\,\!}
⋃
n
=
1
∞
S
n
{\displaystyle \bigcup \limits _{n=1}^{\infty }S_{n}}
Se
f
:
X
→
Y
{\displaystyle f:X\rightarrow Y\,\!}
se
S
{\displaystyle S\,\!}
X
{\displaystyle X\,\!}
f
(
S
)
{\displaystyle f(S)\,\!}
Y
{\displaystyle Y\,\!}
se
T
{\displaystyle T\,\!}
Y
{\displaystyle Y\,\!}
f
−
1
(
T
)
{\displaystyle f^{-1}(T)\,\!}
X
{\displaystyle X\,\!}
O invólucro convexo de um equilibrado de
X
{\displaystyle X\,\!}
Ao menor equilibrado de
X
{\displaystyle X\,\!}
S
{\displaystyle S\,\!}
invólucro equilibrado de
S
{\displaystyle S\,\!}
{
λ
x
:
x
∈
S
,
|
λ
|
≤
1
}
{\displaystyle \{\lambda x:x\in S,|\lambda |\leq 1\}}
O invólucro equilibrado de um subconjunto de
X
{\displaystyle X\,\!}
K
{\displaystyle \mathbb {K} }
X
=
C
{\displaystyle X=\mathbb {C} }
S
=
{
1
}
{\displaystyle S=\{1\}\,\!}
[
−
1
,
1
]
{\displaystyle [-1,1]\,\!}
X
{\displaystyle X\,\!}
S
{\displaystyle S\,\!}
![{\displaystyle [-1,1]\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7f6adf3a2cce8897cbeab299d7a8bfb9f5505896)