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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.23 n.3 Antofagasta dic. 2004

http://dx.doi.org/10.4067/S0716-09172004000300003 

 

Proyecciones
Vol. 23, No 3, pp. 235-240, December 2004.
Universidad Católica del Norte
Antofagasta - Chile

UNIFORM BOUNDEDNESS IN VECTOR - VALUED SEQUENCE SPACES

 

CHARLES SWARTZ

New Mexico State University, USA

Correspondencia a:


ABSTRACT

  

Let µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences c = {ck} such that {q(ck)} ε{X} for all q Î X. The space µ{X} is given the locally convex topology generated by the semi-norms ðppq(c) = p({q(ck)}), p Î X, q Î M. We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the â-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X}.


References

  

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[6] C. Swartz, Introduction to Functional Analysis, Marcel Dekkar, N. Y., (1992).        [ Links ]

[7] C. Swartz, Infinite Matrices and the Gliding Hump, World. Sci. Publ., Singapore, (1996).        [ Links ]

[8] C. Swartz, A Multiplier Gliding hump Property for Sequence Spaces, Proyecciones Revista de Matemática, Vol. 20, pp. 19-31, (2001).        [ Links ]

[9] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, N. Y., (1978).        [ Links ]

 

Received : July 2004. Accepted : November 2004

Charles Swartz
Department of Mathematical Sciences
New Mexico State University
Las Cruces, NM 88003
USA
e-mail : cswartz@nmsu.edu

 

 

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