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Some new sequence spaces which include the spaces lp and l infinity

Aydin C., Başar F.

Demonstratio Mathematica

2005

Vol. 38, nr 3

641--656

In the present paper, we introduce the sequence space apr of non-absolute type and prove that the spaces apr and lp are linearly isomorphic for 0 < p < oo. We also show that apr which includes the space Lp, is a p-normed space and a BK space in the cases of 0 < p < 1 and 1 < p < oo, respectively. Furthermore, we give some inclusion relations and determine the alfa-, beta- and gamma-duals of the space Op and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space arp to some of the known sequence spaces and to some new sequence spaces.

Generalizations of the c0-l1-l∞ theorem of Bessaga and Pełczyński

Wójtowicz M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 4

373-382

Let X and Y be two Banach spaces such that Y has a subsymmetric Schauder basis (yn). We study the consequences of the following assumption: X* has a subspace isomorphic to Y. If the basis is shrinking, then X* contains a copy of Y** (Proposition 1), and if X has the so-called controlled separable projection property (in particular, if X is weakly compactly determined), then X* contains a copy of [yn*]* (Theorem 1). These results are applied for Orlicz sequence spaces.

Haar system as a Schauder basis in Lp(x,y),q(y) (I)

Pietrzyk B.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

1998

[Z] 38

109-114

In this paper we define Lp(x,y),q(y) (I). We investigate some condition of this space.