最終更新日：2022/12/24
The dual space of a Banach space X is the vector space of continuous linear functions X→ℝ, which are called functionals. Similar notation is used for duality pairing between the Banach space X and its dual space X': ⟨u,v⟩ is the result of applying the functional u∈X' to v∈X: ⟨u,v⟩=u(v) explicitly uses the fact that u is a function X→ℝ.
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元となった例文
The
dual
space
of
a
Banach
space
X
is
the
vector
space
of
continuous
linear
functions
X→ℝ,
which
are
called
functionals.
Similar
notation
is
used
for
duality
pairing
between
the
Banach
space
X
and
its
dual
space
X':
⟨u,v⟩
is
the
result
of
applying
the
functional
u∈X'
to
v∈X:
⟨u,v⟩=u(v)
explicitly
uses
the
fact
that
u
is
a
function
X→ℝ.
