-
functional analysis, a
seminorm is a norm that need not be
positive definite.
Seminorms are
intimately connected with
convex sets:
every seminorm is the Minkowski...
-
Unlike seminorms, a
sublinear function does not have to be nonnegative-valued and also does not have to be
absolutely homogeneous.
Seminorms are themselves...
-
continuous seminorms on X {\displaystyle X} , then P {\displaystyle {\mathcal {P}}} is
called a base of
continuous seminorms if it is a base of
seminorms for...
- is
complete with
respect to the
family of
seminorms. A
family P {\displaystyle {\mathcal {P}}} of
seminorms on X {\displaystyle X}
yields a Hausdorff...
- in particular,
every norm is also a
seminorm (and thus also a
sublinear functional). However,
there exist seminorms that are not norms.
Properties (1.)...
- of (continuous)
seminorms. The
topology of X {\displaystyle X} is
induced by a
countable increasing sequence of (continuous)
seminorms ( p i ) i = 1 ∞...
- that it
gives rise to a
seminorm rather than a
vector space norm. The
quotient of this
space by the
kernel of this
seminorm is also
required to be a...
- all
seminorms p {\displaystyle p} ; it is
sufficient to
check it for a set of
seminorms that
generate the topology, in
other words, a set of
seminorms that...
- all
locally convex,
which implies that they are
defined by a
family of
seminorms. In analysis, a
topology is
called strong if it has many open sets and...
- is
generated by a
family of
seminorms {pα | α ∈ A}
where A is an
index set. Let M be a
closed subspace, and
define seminorms qα on X/M by q α ( [ x ] )...
