On Pairs of l-Köthe Spaces

Authors : Erdal KARAPINAR

Pages : 337-349

View : 25 | Download : 8

Publication Date : 2010-03-01

Article Type : Research Paper

Abstract :Let ℓ be a Banach sequence space with a monotone norm k · kℓ, in which the canonical system insert ignore into journalissuearticles values(ei); is a normalized unconditional basis. Let a = insert ignore into journalissuearticles values(ai);, ai → ∞, λ = insert ignore into journalissuearticles values(λi); be sequences of positive numbers. We study the problem on isomorphic classification of pairs F = K ℓ exp − 1 p ai , Kℓ exp − 1 p ai + λi . For this purpose, we consider the sequence of so-called m-rectangle characteristics µ F m. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type ℓ-power series spaces. By using analytic scale and a modification of some invariants insert ignore into journalissuearticles values(modified compound invariants); it is proven that m-rectangular characteristics are invariant on the class of such pairs. Deriving the characteristic βe from the characteristic β, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta insert ignore into journalissuearticles values(Pair of finite type power series spaces, Note di Mathematica 17, 121–142, 1997);.
Keywords : m rectangular characteristic, Power ℓ K¨othe spaces, Linear topological invariants, 2000 AMS Classification 46 A 45