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On the complemented subspaces of the Schreier spaces

100%

Gasparis I., Leung D. H.

Studia Mathematica

2000

tom 141

nr 3

273-300

It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space $X^ξ$ generated by subsequences $(e_{l_n}^{ξ})$ and $(e_{m_n}^{ξ})$, respectively, of the natural Schauder basis $(e_{n}^{ξ})$ of $X^ξ$ are isomorphic if and only if $(e_{l_n}^{ξ})$ and $(e_{m_n}^{ξ})$ are equivalent. Further, $X^ξ$ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of $(e_{n}^{ξ})$. It is also shown that there exists a complemented subspace spanned by a block basis of $(e_{n}^{ξ})$, which is not isomorphic to a subspace generated by a subsequence of $(e_n^ζ)$, for every $0 ≤ ζ ≤ ξ$. Finally, an example is given of an uncomplemented subspace of $X^ξ$ which is spanned by a block basis of $(e_{n}^{ξ})$.

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On the mutually non isomorphic $l_{p}(l_{q})$

80%

Cembranos P., Mendoza J.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2016

tom 36

nr 1

117-127

In this note we survey the partial results needed to show the following general theorem: ${l_{p}(l_{q}) : 1 ≤ p,q ≤ +∞}$ is a family of mutually non isomorphic Banach spaces. We also comment some related facts and open problems.

The space of real-analytic functions has no basis

61%

Domański P., Vogt D.

Studia Mathematica

2000

tom 142

nr 2

187-200

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.

Ograniczanie wyników

2 Studia Mathematica

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Cembranos P.

1 Domański P.

1 Gasparis I.

1 Leung D. H.

1 Mendoza J.

1 Vogt D.

1 2016

2 2000

Wyniki wyszukiwania

On the complemented subspaces of the Schreier spaces

On the mutually non isomorphic $l_{p}(l_{q})$

The space of real-analytic functions has no basis