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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

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.

On generalized Bergman spaces

100%

Lusky W.

Studia Mathematica

1996

tom 119

nr 1

77-95

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 $ʃ_{0}^{1} (ʃ_{0}^{2π} |f(re^{iφ})|^p dφ)^{q/p} dμ(r) < ∞$.

Three-space problems and bounded approximation properties

100%

Lusky W.

tom 159

nr 3

417-434

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.

Bounded operators on weighted spaces of holomorphic functions on the upper half-plane

63%

Ardalani M. , Lusky W.

Studia Mathematica

2012

tom 209

nr 3

225-234

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).

Toeplitz operators on Bergman spaces and Hardy multipliers

63%

Lusky W. , Taskinen J.

nr 2

137-154

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.

On L₁-subspaces of holomorphic functions

63%

Harutyunyan A. , Lusky W.

tom 198

nr 2

157-175

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.

A note on rotation in separable Banach spaces

26%

Lusky W.

Studia Mathematica

1979

tom 65

nr 3

239-242