On the classes of hereditarily $\ell_p$ Banach spaces

Azimi, P.; Ledari, A. A.

Geodesic

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On the classes of hereditarily

ℓ_{p}

Banach spaces

Azimi, P. ; Ledari, A. A.

Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1001-1009.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

Let

X

denote a specific space of the class of

X_{α, p}

Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily

ℓ_{p}

Banach spaces. We show that for

p > 1

the Banach space

X

contains asymptotically isometric copies of

ℓ_{p}

. It is known that any member of the class is a dual space. We show that the predual of

X

contains isometric copies of

ℓ_{q}

where

\frac{1}{p} + \frac{1}{q} = 1

. For

p = 1

it is known that the predual of the Banach space

X

contains asymptotically isometric copies of

c_{0}

. Here we give a direct proof of the known result that

X

contains asymptotically isometric copies of

ℓ_{1}

MR Zbl

Classification : 46B04, 46B20, 46B25
Mots-clés : Banach spaces; asymptotically isometric copy of

ℓ_{p}

; hereditarily

ℓ_{p}

Banach spaces

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     author = {Azimi, P. and Ledari, A. A.},
     title = {On the classes of hereditarily $\ell_p$ {Banach} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1001--1009},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2006},
     mrnumber = {2261672},
     zbl = {1164.46304},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_3_a18/}
}

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Azimi, P.; Ledari, A. A. On the classes of hereditarily $\ell_p$ Banach spaces. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1001-1009. https://geodesic-test.mathdoc.fr/item/CMJ_2006__56_3_a18/