Characterizations of a class of matrix transformations

• Junde, Wu ^[2] ; Wei, Chen ^[2] ; Ronglu, Li ^[1]
  1. [1] Harbin Institute of Technology

     Harbin Institute of Technology

     China

     
  2. [2] Daqing Petroleum Institute.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 17, Nº. 1, 1998, págs. 1-11
• Idioma: inglés
• DOI: 10.22199/S07160917.1998.0001.00001
• Enlaces
  • Texto completo
• Resumen

  • One of the important investigations in the theory of summability is that of finding characterizations on an infinite matrix in order that the matrix should transform one sequence into another sequence space. In this note we present an abstract matrix transformation theorem. Prom it we can obtain the characterizations of a class of matrix transformations.

• Referencias bibliográficas
  • Citas 1. P. Antosik and C. Swartz, Matrix Methods in Analysis, Springer Lecture Notes in Mathematics 1113, Heidelberg, 1985.
  • J. Batt, Applications of the Orlics-Pettis theorem to operator-valued measures and compact and weakly compact linear transformations on the...
  • C. Bessaga and A. Pelczynski, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17, pp. 151 - 164, (1958).
  • D. J. H. Garling, On topological sequence spaces, Proc. Camb. Phil. Soc. 63, pp. 997- 1019, (1967).
  • Li Ronglu and Bu Qingying, Locally convex space containing no copy of co, J. Math. Anal. Appl. 172, pp. 205-211, (1993).
  • Li Ronglu and Cho Minhyung, Bounded multiplier convergent series and applications, Bull. Korean Math. Soc. 29, pp. 215-220, (1992).
  • Li Ronglu and C. Swartz, Spaces for which the uniform boundedness principle holds, Sudia Sci. Math. Hung. 27, pp. 379- 384, (1992).
  • Li Ronglu and C. Swartz, A nonlinear Schur theorem, Acta Sci. Math. (Szeged) 58, pp. 497- 508, (1993).
  • I. Maddox, Schur's theorem for operators, Bull. Soc. Math. Crece 16, pp. 18-21, (1975).
  • Maddox, Infinite matrices of operators, Springer Lecture Notes in Mathematics 786, Heidelberg, (1980).
  • D. Noll, Sequential completeness and spaces with the gliding humps property, Manuscripta Math. 66, pp. 237- 252, (1990).
  • R. Rolewicz, Matric linear spaces, Polish Sci. Publ., Warsaw, (1972).
  • C. Swartz, The Schur lemma for bounded multiplier convergent series, Math. Ann. 263, pp. 283-288, (1983).
  • C. Swartz, The Schur lemma and Hahn Theorems for operators matrices, Rocky Mountain J. Math. 15, pp. 61 - 73, (1985).
  • C. Swartz, The gliding hump property in vector sequence spaces, Monatsh. fur Math. 116, pp. 147- 158, (1993).
  • C. Swartz, Infinite Matrices and the Gliding Hump, World Sci. Publ., Singapore, (1996).
  • B. L. D. Thorp, Sequential-evaluation convergence, J. London Math. Soc. 44, pp. 201 - 209, (1969).