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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 ∥ · ∥ ℓ , in which the canonical system ( e i ) is a normalized symmetric basis. We give a complete isomorphic classification of Cartesian products E 0 ℓ ( a ) × E ∞ ℓ ( b ) where E 0 ℓ ( a ) = K ℓ ( e x p ( - p - 1 a i ) ) and E ∞ ℓ ( b ) = K ℓ ( 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...

Isoperimetric problem for uniform enlargement

S. Bobkov (1997)

Studia Mathematica

We consider an isoperimetric problem for product measures with respect to the uniform enlargement of sets. As an example, we find (asymptotically) extremal sets for the infinite product of the exponential measure.

Iterates and the boundary behavior of the Berezin transform

Jonathan Arazy, Miroslav Engliš (2001)

Annales de l’institut Fourier

Let μ be a measure on a domain Ω in ℂ n such that the Bergman space of holomorphic functions in L 2 ( Ω , μ ) possesses a reproducing kernel K ( x , y ) and K ( x , x ) > 0 ∀ x ∈ Ω . The Berezin transform associated to μ is the integral...

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