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Báo cáo toán học: "Some Results on the Properties D3 (f ) and D4 (f )"

Mục đích của bài viết này là để cho characterizations subspaces và thương số của ∞ (I) ⊗ Π LF (α, ∞) và 1 (I) ⊗ Π LF (α, ∞) không gian là một phần mở rộng của kết quả Apiola [1] cho các trường hợp phi hạt nhân. | Vietnam Journal of Mathematics 34 2 2006 139-147 Viet n a m J o u r n a I of MATHEMATICS VAST 2006 Some Results on the Properties D. f and D. f Pham Hien Bang Department of Mathematics Thai Nguyen University of Education Thai Nguyen Vietnam Received February 17 2005 Revised April 10 2006 Abstract. The aim of this paper is to give characterizations of subspaces and quotients of . .and . .-spaces which are an extension of results of Apiola 1 for the non-nuclear case. 2000 Mathematics subject classification 46A04 46A11 46A32 46A45 Keywords nuclear space . property . property 1. Introduction . Main theorem. Let be a Frechet space. Then has . property if and only if there exists an index set such that is isomorphic to a subspace of - . .-space for every stable nuclear exponent sequence . . . has . property if and only if there exists an index set such that 140 Pham Hien Bang is a quotient of . .-space for every stable nuclear exponent sequence . . 2. Backgrounds ------ . . a . . Some Results on the Properties D . and D . 141 . . . . . . . . . 24 . . . 3. Some Auxiliary Results Proposition 3.1. Let IX . . be an exact sequence of Frechet spaces and continuous linear maps. If D . then the sequence splits. Proof. . . .e. n iei rr 1 Vk 1 rc iei rr 1 rc r rc r rc rc .