Wyniki wyszukiwania

1

Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces

100%

Kühn T., Mastyło M.

Studia Mathematica

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2011

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tom 207

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nr 3

275-296

EN

We investigate how the asymptotic eigenvalue behaviour of Hille-Tamarkin operators in Banach function spaces depends on the geometry of the spaces involved. It turns out that the relevant properties are cotype p and p-concavity. We prove some eigenvalue estimates for Hille-Tamarkin operators in general Banach function spaces which extend the classical results in Lebesgue spaces. We specialize our results to Lorentz, Orlicz and Zygmund spaces and give applications to Fourier analysis. We are also able to show the optimality of our eigenvalue estimates in the Lorentz spaces $L_{2,q}$ with 1 ≤ q < 2 and in Zygmund spaces $L_{p}(log L)_a$ with 2 ≤ p < ∞ and a > 0.

2

Extreme points of the complex binary trilinear ball

81%

Cobos F., Kühn T., Peetre J.

Studia Mathematica

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2000

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tom 138

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nr 1

81-92

EN

We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space $ℂ^2$. This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space $ℝ^2$. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

3

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On the dependence of parameters in the equivalence theorem for the real method

81%

Cobos F., Fernández-Cabrera L. M., Karadzhov G. E., Kühn T.

Commentationes Mathematicae

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2015

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tom 55

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nr 2

EN

We determine the exact dependence on $\theta,q,p$ of the constants in the equivalence theorem for the real interpolation method $(A_0,A_1)_{\theta,q}$ with pairs of $p$-normed spaces.

4

Entropy numbers of r-nuclear operators in Banach spaces of type q

50%

Kühn T.

Studia Mathematica

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1984

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tom 80

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nr 1

53-61

Ograniczanie wyników

3 Studia Mathematica

1 Commentationes Mathematicae

4 Kühn T.

2 Cobos F.

1 Fernández-Cabrera L. M.

1 Karadzhov G. E.

1 Mastyło M.

1 Peetre J.

1 2015

1 2011

1 2000

1 1984

Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces

Extreme points of the complex binary trilinear ball

On the dependence of parameters in the equivalence theorem for the real method

Entropy numbers of r-nuclear operators in Banach spaces of type q