Analysis MOC

Seminormed vector space

A seminormed vector space is a Vector space over a Subfield of equipped with a seminorm , a weakening of a norm satisfying the following conditions for any and #m/def/anal/vec

1. Absolute homogeneity:
2. Triangle inequality:

whence follows

3. Nonnegativity:

By strengthening nonnegativity to positive-definiteness the seminorm becomes a full norm.

Properties

1. A seminorm induces a normed quotient

#state/tidy | #lang/en | #SemBr