Uniform Boundedness Principle

In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.

The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus but it was also proven independently by Hans Hahn.

Read more about Uniform Boundedness Principle:  Uniform Boundedness Principle, Generalizations

Famous quotes containing the words uniform and/or principle:

    The sugar maple is remarkable for its clean ankle. The groves of these trees looked like vast forest sheds, their branches stopping short at a uniform height, four or five feet from the ground, like eaves, as if they had been trimmed by art, so that you could look under and through the whole grove with its leafy canopy, as under a tent whose curtain is raised.
    Henry David Thoreau (1817–1862)

    The principle of majority rule is the mildest form in which the force of numbers can be exercised. It is a pacific substitute for civil war in which the opposing armies are counted and the victory is awarded to the larger before any blood is shed. Except in the sacred tests of democracy and in the incantations of the orators, we hardly take the trouble to pretend that the rule of the majority is not at bottom a rule of force.
    Walter Lippmann (1889–1974)