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1
Content available remote Spaces of Whitney jets on self-similar sets
100%
Vogt D.
|
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tom 218
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nr 1
89-94
EN
It is shown that complemented subspaces of s, that is, nuclear Fréchet spaces with properties (DN) and (Ω), which are 'almost normwise isomorphic' to a multiple direct sum of copies of themselves are isomorphic to s. This is applied, for instance, to spaces of Whitney jets on the Cantor set or the Sierpiński triangle and gives new results and also sheds new light on known results.
2
Content available remote Non-natural topologies on spaces of holomorphic functions
100%
Vogt D.
|
2013
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tom 108
|
nr 3
215-217
EN
It is shown that every proper Fréchet space with weak*-separable dual admits uncountably many inequivalent Fréchet topologies. This applies, in particular, to spaces of holomorphic functions, solving in the negative a problem of Jarnicki and Pflug. For this case an example with a short self-contained proof is added.
3
Content available remote The tensor algebra of power series spaces
100%
Vogt D.
Studia Mathematica
|
2009
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tom 193
|
nr 2
189-202
EN
The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra $s_{•}$. This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras with (Ω) as quotient algebras of $s_{•}$ and Fréchet m-algebras with (DN) and (Ω) as quotient algebras of $s_{•}$ with respect to a complemented ideal.
4
Content available remote Construction of standard exact sequences of power series spaces
63%
Poppenberg M. , Vogt D.
Studia Mathematica
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1994-1995
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tom 112
|
nr 3
229-241
XX
The following result is proved: Let $Λ_R^p(α)$ denote a power series space of infinite or of finite type, and equip $Λ_R^p(α)$ with its canonical fundamental system of norms, R ∈ {0,∞}, 1 ≤ p < ∞. Then a tamely exact sequence (⁎) $0 → Λ_{R}^{p}(α) → Λ_{R}^{p}(α) → Λ_{R}^{p}(α)^ℕ → 0$ exists iff α is strongly stable, i.e. $lim_n α_{2n}/α_n = 1$, and a linear-tamely exact sequence (*) exists iff α is uniformly stable, i.e. there is A such that $lim sup_n α_{Kn}/α_n ≤ A < ∞$ for all K. This result extends a theorem of Vogt and Wagner which states that a topologically exact sequence (*) exists iff α is stable, i.e. $sup_n α_{2n}/α_n < ∞$.
5
Content available remote The space of real-analytic functions has no basis
63%
Domański P. , Vogt D.
Studia Mathematica
|
2000
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tom 142
|
nr 2
187-200
EN
Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.
6
Content available remote Fréchet spaces with quotients failing the bounded approximation property
44%
Dubinsky E. , Vogt D.
Studia Mathematica
|
1985
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tom 81
|
nr 1
71-77
7
Content available remote Charakterisierung der Unterraüme und Quotienteräume der nuklearen stabilen Potenzreihenraüme von unendlichem Typ
44%
Vogt D. , Wagner M. J.
|
|
nr 1
63-80
8
Content available remote Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces
44%
Meise R. , Vogt D.
Studia Mathematica
|
1986
|
tom 83
|
nr 2
147-166
9
Content available remote Complemented subspaces in tame power series spaces
38%
Dubinsky E. , Vogt D.
|
|
tom 93
|
nr 1
71-85
10
Content available remote Charakterisierung der Quotientenräume von s und eine Vermutung von Martineau
32%
Vogt D. , Wagner M. J.
|
|
tom 67
|
nr 3
225-240
11
Content available remote On the functors Ext¹(E,F) for Fréchet spaces
32%
Vogt D.
Studia Mathematica
|
1987
|
tom 85
|
nr 2
163-197
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