Abstract:We study the structure of complemented subspaces in Cartesian products X × Y of Köthe spaces X and Y under the assumption that every linear continuous operator from X to Y is bounded. In particular, it is proved that each non-Montel complemented subspace with absolute basis E ⊂ X × Y is isomorphic to a space of the form E1 × E2 , where E1 is a complemented subspace of X and E2 is a complemented subspace of Y.
In this manuscript, we investigate the isomorphisms of OrliczKöthe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.Mathematics Subject Classification (2010). Primary 46A45; Secondary 46B45.
In this manuscript, we investigate the isomorphisms of OrliczKöthe sequence spaces and quasidiagonal isomorphisms of Cartesian products of Orlicz-power series spaces.Mathematics Subject Classification (2010). Primary 46A45; Secondary 46B45.
“…The spaces λ p (A), 1 < p ≤ ∞ are called as generalized Köthe spaces by Bierstedt et al [1]. In some sources, for example [3,7], the spaces λ p (A) denoted by K p (A) and called by p −Köthe space for 1 ≤ p < ∞.…”
Section: Introductionmentioning
confidence: 99%
“…Equipped with semi-norms given by (1) K (A) is a Fréchet space, [3]. It is well-known that the space bs of bounded series is defined by…”
Section: Introductionmentioning
confidence: 99%
“…and is an admissible space with the norm • bs . Following [3,7], we define the new space λ bs (A) by…”
Let A = (a nk) be a Köthe matrix. In this paper, we introduce the space λ bs (A) and we emphasize on some topological properties of the spaces c 0 (A), λ bs (A) and λ p (A) together with some inclusion relations, where 1 ≤ p ≤ ∞.
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