Continuous Linear Extension
In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space by first defining a linear transformation on a dense subset of and then extending to the whole space via the theorem below. The resulting extension remains linear and bounded (thus continuous).
This procedure is known as continuous linear extension.
Read more about Continuous Linear Extension: Theorem, Application, The Hahn–Banach Theorem
Famous quotes containing the words continuous and/or extension:
“Perhaps when distant people on other planets pick up some wave-length of ours all they hear is a continuous scream.”
—Iris Murdoch (b. 1919)
“Where there is reverence there is fear, but there is not reverence everywhere that there is fear, because fear presumably has a wider extension than reverence.”
—Socrates (469–399 B.C.)