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Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

100%

Karapınar E., Yurdakul M., Zahariuta V.

Bulletin of the Polish Academy of Sciences. Mathematics

2006

tom 54

nr 2

103-111

Let ℓ be a Banach sequence space with a monotone norm $∥·∥_{ℓ}$, in which the canonical system $(e_i)$ is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products $E^{ℓ}_{0}(a) × E^{ℓ}_{∞}(b)$ where $E^{ℓ}_{0}(a) = K^{ℓ}(exp(-p^{-1}a_i))$ and $E^{ℓ}_{∞}(b) = K^{ℓ}(exp(pa_i))$ are finite and infinite ℓ-power series spaces, respectively. This classification is the generalization of the results by Chalov et al. [Studia Math. 137 (1999)] and Djakov et al. [Michigan Math. J. 43 (1996)] by using the method of compound linear topological invariants developed by the third author.

Factorization of unbounded operators on Köthe spaces

100%

Terzioğlu T., Yurdakul M., Zahariuta V.

Studia Mathematica

2004

tom 161

nr 1

61-70

The main result is that the existence of an unbounded continuous linear operator T between Köthe spaces λ(A) and λ(C) which factors through a third Köthe space λ(B) causes the existence of an unbounded continuous quasidiagonal operator from λ(A) into λ(C) factoring through λ(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (λ(A),λ(B)) ∈ ℬ (which means that all continuous linear operators from λ(A) to λ(B) are bounded). The proof is based on the results of [9] where the bounded factorization property ℬ F is characterized in the spirit of Vogt's [10] characterization of ℬ. As an application, it is shown that the existence of an unbounded factorized operator for a triple of Köthe spaces, under some additonal asumptions, causes the existence of a common basic subspace at least for two of the spaces (this is a factorized analogue of the results for pairs [8, 2]).

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Studia Mathematica

2 Yurdakul M.

2 Zahariuta V.

1 Karapınar E.

1 Terzioğlu T.

1 2006

1 2004

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Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

Factorization of unbounded operators on Köthe spaces