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Sätze vom Mazur-Orlicz-Typ. (English) Zbl 0611.46006
The main result of the paper is a theorem of Mazur-Orlicz type which says that \(X\cap W_ A\subset c_ B\) implies \(X\cap W_ A\subset W_ B\) if only the domains \(c_ A\) and \(c_ B\) of the (infinite) matrices A and B contain the set of finite sequences and X is an FK-AB-space with certain factor sequences (for example, if X is a solid FK-AB-space). G. Bennett and N. J. Kalton [Duke Math. J. 39, 561-582 (1972; Zbl 0245.46011) and Trans. Am. Math. Soc. 198, 23-43 (1974; Zbl 0301.46005)] proved theorems of this kind in case of special spaces X and FK-spaces E (instead of \(c_ A)\) containing \(c_ 0\). More general than the results of Bennett and Kalton, A. K. Snyder [Stud. Math. 71, 1-26 (1982; Zbl 0524.46003)] proved a theorem of this kind in case of semiconservative FK-spaces E and sequence spaces X fulfilling strong conditions which are connected with the space E.
As corollaries of the main result we get new and known consistency theorems, for example the bounded consistency theorem of S. Mazur and W. Orlicz [Stud. Math. 14, 129-160 (1955; Zbl 0064.056)].

MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
40D15 Convergence factors and summability factors
40D20 Summability and bounded fields of methods
40H05 Functional analytic methods in summability
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
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