Matrix summability and uniform convergence of series

Aizpuru, Antonio; García-Pacheco, Francisco; Pérez-Eslava, Consuelo

doi:10.1090/S0002-9939-07-08882-X

Matrix summability and uniform convergence of series
HTML articles powered by AMS MathViewer

by Antonio Aizpuru, Francisco J. García-Pacheco and Consuelo Pérez-Eslava PDF

Proc. Amer. Math. Soc. 135 (2007), 3571-3579 Request permission

Abstract:

Some classical results about uniform convergence of unconditionally convergent series are generalized to weakly unconditionally Cauchy series by means of the matrix summability method for regular matrices.

References

A. Aizpuru and J. Pérez-Fernández, Spaces of $\scr S$-bounded multiplier convergent series, Acta Math. Hungar. 87 (2000), no. 1-2, 135–146. MR 1755883, DOI 10.1023/A:1006781218759
A. Aizpuru, A. Gutiérrez-Dávila, and F. J. Pérez-Fernández, Boolean algebras and uniform convergence of series, J. Math. Anal. Appl. 284 (2003), no. 1, 89–96. MR 1996119, DOI 10.1016/S0022-247X(03)00241-5
A. Aizpuru and C. Pérez-Eslava, Matrix methods in summability and weakly unconditionally Cauchy series, Preprint.
C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 115069, DOI 10.4064/sm-17-2-151-164
Johann Boos, Classical and modern methods in summability, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2000. Assisted by Peter Cass; Oxford Science Publications. MR 1817226
Qingying Bu and Congxin Wu, Unconditionally convergent series of operators on Banach spaces, J. Math. Anal. Appl. 207 (1997), no. 2, 291–299. MR 1438915, DOI 10.1006/jmaa.1997.5218
Joseph Diestel, Sequences and series in Banach spaces, Graduate Texts in Mathematics, vol. 92, Springer-Verlag, New York, 1984. MR 737004, DOI 10.1007/978-1-4612-5200-9
Joe Diestel, Hans Jarchow, and Andrew Tonge, Absolutely summing operators, Cambridge Studies in Advanced Mathematics, vol. 43, Cambridge University Press, Cambridge, 1995. MR 1342297, DOI 10.1017/CBO9780511526138
Richard Haydon, A nonreflexive Grothendieck space that does not contain $l_{\infty }$, Israel J. Math. 40 (1981), no. 1, 65–73. MR 636907, DOI 10.1007/BF02761818
Walter Schachermayer, On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras, Dissertationes Math. (Rozprawy Mat.) 214 (1982), 33. MR 673286
Charles Swartz, The Schur lemma for bounded multiplier convergent series, Math. Ann. 263 (1983), no. 3, 283–288. MR 704294, DOI 10.1007/BF01457131