On Pairs of l-Köthe Spaces

Year 2010, Volume: 39 Issue: 3, 337 - 349, 01.03.2010

Erdal Karapınar

Abstract

Let ℓ be a Banach sequence space with a monotone norm k · kℓ, in
which the canonical system (ei) is a normalized unconditional basis.
Let a = (ai), ai → ∞, λ = (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 (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 (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

On Pairs of l-Köthe Spaces

Abstract

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