References
S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
G. Bennett, J. Sember, A. Wilansky, Sections of sequences in matrix domains (to appear).
H. I. Brown, The summability field of a perfectl−l method of summation,Journal d'Analyse Mathématique,20 (1967), 281–287.
H. I. Brown and V. F. Cowling, On the consistency ofl−l methods of summation,Michigan Math. J.,12 (1965), 357–362.
J. Copping, Inclusion theorems for conservative summation methods,Kon. Ned. Akad. Wetensch., (A)61 (1958), 487–499.
D. J. Fleming and P. G. Jessup, Perfect matrix methods,Proc. Amer. Math. Soc.,29 (1971), 319–324.
D. J. H. Garling, The β- and γ-duality of sequence spaces,Proc. Cambridge Phil. Soc.,63 (1967), 963–981.
D. J. H. Garling, On topological sequence spaces,Proc. Cambridge Phil. Soc.,63 (1967), 997–1019.
A. Jakimovski and A. Livne, General Kojima-Toeplitz like theorems and consistency theorems,J. d'Anal. Math.,24 (1971), 323–368.
A. Jakimovski and A. Livne, On matrix transformations between sequence spaces,J. d'Anal. Math.,25 (1972), 345–370.
A. Jakimovski and D. C. Russell, Matrix mappings between BK-spacesBulletin London Math. Soc.,4 (1972).
S. Mazur, Über lineare Limitierungsverfahren,Math. Zeit.,28 (1928), 599–611.
A. Peyerimhoff, Untersuchungen über absolute Summierbarkeit,Math. Zeit.,57 (1953), 265–290.
D. C. Russell, Note on inclusion theorems for infinite matrices,J. London Math. Soc.,33 (1958), 50–62.
D. C. Russell, Inclusion theorems for section-bounded matrix transformations,Math. Zeit.,113 (1970), 255–265.
W. L. C. Sargent, On sectionally bounded BK-spaces,Math. Zeit.,83 (1964), 57–66.
J. J. Sember, The associative part of a convergence domain is invariant,Canad. Math. Bull.,13 (1970), 147–148.
A. Wilansky, Functional Analysis, New York, 1964.
A. Wilansky, Distinguished subsets and summability invariants,J. d'Anal. Math.,12 (1964), 327–350.
A. Wilansky and K. Zeller, Abschnittsbeschränkte Matrixtransformationen; starke Limitierbarkeit,Math. Zeit.,64 (1965), 258–269.
K. Zeller, Abschnittskonvergenz in FK-Räumen,Math. Zeit.,55 (1951), 55–70.
K. Zeller, Allgemeine Eigenschaften von Limitierungsverfahren,Math. Zeit.,53 (1951), 463–487.
K. Zeller and W. Beekmann, Theorie der Limitierungsverfahren, Springer, Berlin, 2nd. edition 1970.
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Jakimovski, A., Russell, D.C. & Tzimbalario, J. Inclusion theorems for matrix transformations. J. Anal. Math. 26, 391–404 (1973). https://doi.org/10.1007/BF02790436
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DOI: https://doi.org/10.1007/BF02790436