Wyniki wyszukiwania

1

On approximation by special analytic polyhedral pairs

100%

Zahariuta V.

Annales Polonici Mathematici

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2003

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tom 80

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nr 1

243-256

EN

For bounded logarithmically convex Reinhardt pairs "compact set - domain" (K,D) we solve positively the problem on simultaneous approximation of such a pair by a pair of special analytic polyhedra, generated by the same polynomial mapping f: D → ℂⁿ, n = dimΩ. This problem is closely connected with the problem of approximation of the pluripotential ω(D,K;z) by pluripotentials with a finite set of isolated logarithmic singularities ([23, 24]). The latter problem has been solved recently for arbitrary pluriregular pairs "compact set - domain" (K,D) by Poletsky [12] and S. Nivoche [10, 11], while the first one is still open in the general case.

2

Width asymptotics for a pair of Reinhardt domains

51%

Aytuna A., Rashkovskii A., Zahariuta V.

Annales Polonici Mathematici

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2002

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tom 78

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nr 1

31-38

EN

For complete Reinhardt pairs "compact set - domain" K ⊂ D in ℂⁿ, we prove Zahariuta's conjecture about the exact asymptotics $ln d_s(A_K^D) ~ -((n!s)/τ(K,D))^{1/n}$, s → ∞, for the Kolmogorov widths $d_s(A_K^D)$ of the compact set in C(K) consisting of all analytic functions in D with moduli not exceeding 1 in D, τ(K,D) being the condenser pluricapacity of K with respect to D.

3

Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

51%

Karapınar E., Yurdakul M., Zahariuta V.

Bulletin of the Polish Academy of Sciences. Mathematics

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2006

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tom 54

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nr 2

103-111

EN

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.

4

Factorization of unbounded operators on Köthe spaces

51%

Terzioğlu T., Yurdakul M., Zahariuta V.

Studia Mathematica

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2004

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tom 161

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nr 1

61-70

EN

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

2 Annales Polonici Mathematici

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Studia Mathematica

4 Zahariuta V.

2 Yurdakul M.

1 Aytuna A.

1 Karapınar E.

1 Rashkovskii A.

1 Terzioğlu T.

1 2006

1 2004

1 2003

1 2002

On approximation by special analytic polyhedral pairs

Width asymptotics for a pair of Reinhardt domains

Isomorphisms of Cartesian Products of ℓ-Power Series Spaces

Factorization of unbounded operators on Köthe spaces