An abstract Orlics-Pettis theorem and applications

  • Li Ronglu Harbin Institute of Technology.
  • Charles Swartz New Mexico State University.
Palabras clave: Topological vector space, locally convex spaces, convergent series, operators, espacios vectoriales topológicos, espacios localmente convexos, series convergentes, operadores.

Resumen

In this paper we establish two abstract versions of the classical Orlicz-Pettis Theorem for multiplier convergent series. We show that these abstract results yield known versions of the Orlicz-Pettis Theorem for locally convex spaces as well as versions for operator valued series. We also give applications to vector valued measures and spaces of continuous functions.

Biografía del autor

Li Ronglu, Harbin Institute of Technology.
Department of Mathematics.
Charles Swartz, New Mexico State University.
Department of Mathematics.

Citas

[BSS] H. Boos, C. Stuart and C. Swartz, Gliding Hump Properties and Matrix Domains, Analysis Math., 30, pp. 243-257, (2004).

[DS] N. Dunford and J. Schwartz, Linear Operators, Interscience, N. Y., (1958).

[E] R. E.Edwards, Functional Analysis, Holt-Rinehart-Winston, N. Y., (1965).

[GR] W. Graves and W. Ruess, Compactness in spaces of vector-valued measures and natural Mackey topology for spaces bounded measurable functions, Contemp. Math., 2, pp. 189-203, (1980).

[K] G. Kothe, Topological Vector Space I, Springer-Verlag, Berlin, (1969).

[LW] E. Lacey and R.J. Whitley, Conditions under which all the Bounded Linear Maps are Compact, Math. Ann., 158, pp. 1-5, (1965).

[N] D. Noll, Sequential Completeness and Spaces with the Gliding Humps Property, Manuscripta Math., 66, pp. 237-252, (1990).

[O] W. Orlicz, Beitrage zur Theorie Orthogonent Wichlungen II, Studia Math. 1, pp. 241-255, (1929).

[P] B. J. Pettis, On Integration in Vector Spaces, Trans. Amer. Math. Soc., 44, pp. 277-304, (1938).

[ST1] C. Stuart, Weak Sequential Completeness in Sequence Spaces, Ph.D. Dissertation, New Mexico state University, (1993).

[ST2] C. Stuart, Weak Sequential Completeness of β-duals, Rocky Mount, J. Math., 26, pp. 1559-1568, (1996).

[SS] C. Stuart and C. Swartz, Generalizations of the Orlicz-Pettis Theorem, Proy. J. Math., 24, pp. 37-48, (2005).

[SW1] C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, (1996).

[SW2] C. Swartz, Uniform Convergence of Multiplier Convergent Series, Proy. J. Math., 26, pp. 27-35, (2007).

[TH] G. E. F. Thomas, L’integration par rapport a une mesure de Radon vectorielle, Ann. Inst. Fourier, 20, pp. 55-191, (1970).

[WL] Wu Junde and Lu Shijie, A General Orlicz-Pettis Theorem, Taiwan. J. Math., 6, pp. 433-440, (2002).
Publicado
2017-05-02
Cómo citar
Ronglu, L., & Swartz, C. (2017). An abstract Orlics-Pettis theorem and applications. Proyecciones. Journal of Mathematics, 27(2), 155-169. https://doi.org/10.4067/S0716-09172008000200003
Sección
Artículos