in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.

Paul Garrett [email protected] http://www.math.umn.edu/ g̃arrett/ [This document is http://www.math.umn.edu/ ̃garrett/m/fun/notes 2012-13/05 banach.pdf] 1. Basic definitions 2. Riesz’ Lemma 3. Counter-example: non-existence of norm-minimizing element 4. Normed spaces of continuous linear maps 5. Dual spaces of normed spaces 6. Banach-Steinhaus/uniform-boundedness theorem 7. Open mapping theore...

1. Basic definitions 2. Riesz’ Lemma 3. Counter-examples for unique norm-minimizing element 4. Normed spaces of continuous linear maps 5. Dual spaces of normed spaces 6. Baire’s theorem 7. Banach-Steinhaus/uniform-boundedness theorem 8. Open mapping theorem 9. Closed graph theorem 10. Hahn-Banach theorem Many natural spaces of functions, such as C(K) for K compact, and C[a, b], have natural str...

A Banach-Steinhaus theorem for sets of continuous linear mappings on topological modules which are Baire spaces is proved, and some consequences of it are derived. Mathematics Subject Classification: 46H25, 46S10, 46E10