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Isomorphic classification of the tensor products E ( e x p α i ) ̂ E ( e x p β j )

Peter Chalov, Vyacheslav Zakharyuta (2011)

Studia Mathematica

It is proved, using so-called multirectangular invariants, that the condition αβ = α̃β̃ is sufficient for the isomorphism of the spaces E ( e x p α i ) ̂ E ( e x p β j ) and E ( e x p α ̃ i ) ̂ E ( e x p β ̃ j ) . This solves a problem posed in [14, 15, 1]. Notice that the necessity has been proved earlier in [14].

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Choban, Mitrofan (1998)

Serdica Mathematical Journal

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first...

Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

E. Karapınar, M. Yurdakul, V. Zahariuta (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Let ℓ be a Banach sequence space with a monotone norm · , in which the canonical system ( e i ) is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products E 0 ( a ) × E ( b ) where E 0 ( a ) = K ( e x p ( - p - 1 a i ) ) and E ( b ) = K ( e x p ( p a 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....

Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces

Manfred Scheve (1991)

Studia Mathematica

Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory...

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