Encyclopedia > Bounded linear operator

Article Content

Bounded linear operator

In functional analysis, a linear transformation L between normed vector spaces is said to be bounded, or to be a bounded linear operator, if the ratio of the norms of L(v) and v is bounded above, over all non-zero vectors v.

It is simple to prove that this is the same condition on L as continuity, for the topologies induced from the norms.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia

Search over one million articles, find something about almost anything!

Featured Article

Jean de la Bruyère

... in the revenue department at Caen, which gave the status of noblesse and a certain income. In 1687 he sold this office. His predecessor in it was a relation of Bossuet, and ...