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1
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On the isomorphism classes of weighted spaces of harmonic and holomorphic functions

100%
Lusky W.
Studia Mathematica
|
2006
|
tom 175
|
nr 1
19-45
EN
Let Ω be either the complex plane or the open unit disc. We completely determine the isomorphism classes of $Hv = {f: Ω → ℂ holomorphic: sup_{z∈ Ω} |f(z)|v(z) < ∞}$ and investigate some isomorphism classes of $hv = {f: Ω → ℂ harmonic : sup_{z∈ Ω} |f(z)|v(z) < ∞}$ where v is a given radial weight function. Our main results show that, without any further condition on v, there are only two possibilities for Hv, namely either $Hv ∼ l_{∞}$ or $Hv ∼ H_{∞}$, and at least two possibilities for hv, again $hv ∼ l_{∞}$ and $hv ∼ H_{∞}$. We also discuss many new examples of weights.
2
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On generalized Bergman spaces

100%
Lusky W.
Studia Mathematica
|
1996
|
tom 119
|
nr 1
77-95
EN
Let D be the open unit disc and μ a positive bounded measure on [0,1]. Extending results of Mateljević/Pavlović and Shields/Williams we give Banach-space descriptions of the classes of all harmonic (holomorphic) functions f: D → ℂ satisfying $ʃ_{0}^{1} (ʃ_{0}^{2π} |f(re^{iφ})|^p dφ)^{q/p} dμ(r) < ∞$.
3
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Every separable L₁-predual is complemented in a C*-algebra

100%
Lusky W.
Studia Mathematica
|
2004
|
tom 160
|
nr 2
103-116
EN
We show that every separable complex L₁-predual space X is contractively complemented in the CAR-algebra. As an application we deduce that the open unit ball of X is a bounded homogeneous symmetric domain.
4
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Three-space problems and bounded approximation properties

100%
Lusky W.
Studia Mathematica
|
2003
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tom 159
|
nr 3
417-434
EN
Let ${Rₙ}_{n=1}^{∞}$ be a commuting approximating sequence of the Banach space X leaving the closed subspace A ⊂ X invariant. Then we prove three-space results of the following kind: If the operators Rₙ induce basis projections on X/A, and X or A is an $ℒ_{p}$-space, then both X and A have bases. We apply these results to show that the spaces $C_{Λ} = \overline{span}{z^{k} : k ∈ Λ} ⊂ C(𝕋)$ and $L_{Λ} = \overline{span}{z^{k} : k ∈ Λ} ⊂ L₁(𝕋)$ have bases whenever Λ ⊂ ℤ and ℤ∖Λ is a Sidon set.
5
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On L₁-subspaces of holomorphic functions

64%
Harutyunyan A., Lusky W.
Studia Mathematica
|
2010
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tom 198
|
nr 2
157-175
EN
We study the spaces $H_{μ}(Ω) = {f: Ω → ℂ holomorphic: ∫_{0}^{R} ∫_{0}^{2π} |f(re^{iφ})| dφdμ(r) < ∞}$ where Ω is a disc with radius R and μ is a given probability measure on [0,R[. We show that, depending on μ, $H_{μ}(Ω)$ is either isomorphic to l₁ or to $(∑ ⊕ Aₙ)_{(1)}$. Here Aₙ is the space of all polynomials of degree ≤ n endowed with the L₁-norm on the unit sphere.
6
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Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

64%
Ardalani M., Lusky W.
Studia Mathematica
|
2012
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tom 209
|
nr 3
225-234
EN
Let v be a standard weight on the upper half-plane 𝔾, i.e. v: 𝔾 → ]0,∞[ is continuous and satisfies v(w) = v(i Im w), w ∈ 𝔾, v(it) ≥ v(is) if t ≥ s > 0 and $lim_{t→ 0} v(it) = 0$. Put v₁(w) = Im wv(w), w ∈ 𝔾. We characterize boundedness and surjectivity of the differentiation operator D: Hv(𝔾) → Hv₁(𝔾). For example we show that D is bounded if and only if v is at most of moderate growth. We also study composition operators on Hv(𝔾).
7
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On the boundedness of the differentiation operator between weighted spaces of holomorphic functions

64%
Harutyunyan A., Lusky W.
Studia Mathematica
|
2008
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tom 184
|
nr 3
233-247
EN
We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
8
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Toeplitz operators on Bergman spaces and Hardy multipliers

64%
Lusky W., Taskinen J.
Studia Mathematica
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2011
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tom 204
|
nr 2
137-154
EN
We study Toeplitz operators $T_{a}$ with radial symbols in weighted Bergman spaces $A_{μ}^{p}$, 1 < p < ∞, on the disc. Using a decomposition of $A_{μ}^{p}$ into finite-dimensional subspaces the operator $T_{a}$ can be considered as a coefficient multiplier. This leads to new results on boundedness of $T_{a}$ and also shows a connection with Hardy space multipliers. Using another method we also prove a necessary and sufficient condition for the boundedness of $T_{a}$ for a satisfying an assumption on the positivity of certain indefinite integrals.
9
Content available remote

A note on rotation in separable Banach spaces

26%
Lusky W.
Studia Mathematica
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1979
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tom 65
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nr 3
239-242
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