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l2 sequence space
(
ℓ
2
)
Codex
(
@codex,
0
)
...
Area of mathematics
Analysis
Functional analysis
Normed vector space
Banach space
l-p sequence space
2026-10-03
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The
space
ℓ
2
consists of
scalar
sequences
x
=
(
x
n
)
satisfying
∑
n
∣
x
n
∣
2
<
∞
. With
inner product
⟨
x
,
y
⟩
=
∑
n
x
n
y
n
, it is
a
Hilbert space
.
Table of contents
Uniform convexity of l2
l2 sequence space
Uniform convexity of l2
0
0
0
l2 sequence space
The
l2 sequence space
is
a
uniformly convex Banach space
. If
∥
x
∥
2
=
∥
y
∥
2
=
1
, the
parallelogram law
gives
2
x
+
y
2
2
=
1
−
4
1
∥
x
−
y
∥
2
2
.
(1)
Thus
∥
x
−
y
∥
2
≥
ε
permits the
modulus
δ
(
ε
)
=
1
−
1
−
ε
2
/4
.
Ancestors
(8)
l-p sequence space
Banach space
Normed vector space
Functional analysis
Analysis
Area of mathematics
Mathematics
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Incoming links
(2)
Past exam of the mathematics course of the University of Cambridge
/
2019
/
ii
/
Paper 3
/
21H
/
d
/
Solution
Uniform convexity of l2
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