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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
Created
2026-10-03
Updated
2026-10-06
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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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Absolutely summing operator
Bounded bilinear form
Coercive bilinear form
Extreme points of real sequence-space unit balls
Hamming cube as an L1 and L2 metric
Heine-Borel theorem
Hilbert space
Hilbert space completion
Infinite-dimensional bounded sequences can lack convergent subsequences
Past exam of the mathematics course of the University of Cambridge
/
2007
/
iii
/
Paper 8
/
2
/
ii
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2008
/
iii
/
Paper 80
/
5
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2015
/
iii
/
Paper 5
/
2
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2017
/
iii
/
Paper 326
/
1
/
2
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2017
/
iii
/
Paper 326
/
4
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2017
/
iii
/
Paper 326
/
4
/
4
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2018
/
iii
/
Paper 326
/
1
/
1
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2018
/
iii
/
Paper 326
/
2
/
2
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2019
/
ii
/
Paper 3
/
21H
/
d
/
Solution
Positive operator
Rademacher function
Rademacher span is not complemented in L1
Spectrum of a bounded operator
Strict positivity without coercivity can fail variational solvability
Subdifferential of a weighted one-norm on l2
Uniform convexity of l2
Weighted one-norm on l2
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