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

Islip Terrace, New York

... For every 100 females age 18 and over, there are 93.6 males. The median income for a household in the town is $66,644, and the median income for a family is $69,389. Males ...