کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4623441 1339516 2006 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dual pairs of sequence spaces. III
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Dual pairs of sequence spaces. III
چکیده انگلیسی

In the previous papers [J. Boos, T. Leiger, Dual pairs of sequence spaces, Int. J. Math. Math. Sci. 28 (2001) 9–23; J. Boos, T. Leiger, Dual pairs of sequence spaces. II, Proc. Estonian Acad. Sci. Phys. Math. 51 (2002) 3–17], the authors defined and investigated dual pairs (E,ES), where E is a sequence space, S is a BK-space on which a sum s is defined in the sense of Ruckle [W.H. Ruckle, Sequence Spaces, Pitman Advanced Publishing Program, Boston, 1981], and ES is the space of all factor sequences from E into S. In generalization of the SAK-property (weak sectional convergence) in the case of the dual pair (E,Eβ), the SK-property was introduced and studied. In this note we consider factor sequence spaces E|S|, where |S| is the linear span of , the closure of the unit ball of S in the FK-space ω of all scalar sequences. An FK-space E such that E|S| includes the f-dual Ef is said to have the SB-property. Our aim is to demonstrate, that in the duality (E,ES), the SB-property plays the same role as the AB-property in the case ES=Eβ. In particular, we show for FK-spaces, in which the subspace of all finitely non-zero sequences is dense, that the SB-property implies the SK-property. Moreover, in the context of the SB-property, a generalization of the well-known factorization theorem due to Garling [D.J.H. Garling, On topological sequence spaces, Proc. Cambridge Philos. Soc. 63 (1967) 997–1019] is given.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 324, Issue 2, 15 December 2006, Pages 1213-1227