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

Bullying

... for someone with absolute governmental power, from the Greek language turannos. In Classical Antiquity[?] it did not always have inherently negative implications, it ...