Banach-Steinhaus theorem

Banach-Steinhaus theorem

[¦bä‚näk ¦stīn‚hau̇s ‚thir·əm]
(mathematics)
If a sequence of bounded linear transformations of a Banach space is pointwise bounded, then it is uniformly bounded.
References in periodicals archive ?
Thus, it follows by the Banach-Steinhaus theorem [24, p.
Hence, by the Banach-Steinhaus theorem there exists a [f.
1 in conjunction with the Banach-Steinhaus theorem implies the useful estimate
tau]T(a)] strongly, the Banach-Steinhaus theorem gives
Then, by the Banach-Steinhaus theorem, we would have supn [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] < [infinity] which is not possible since, again by Proposition 2.
In addition, various topics have been substantially expanded, and new material on weak derivatives and Sobolev spaces, the Hahn-Banach theorem, reflexive Banach spaces, the Banach Schauder and Banach-Steinhaus theorems, and the Lax-Milgram theorem has been incorporated into the book.