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Title: Isomorphic spectrum and isomorphic length of a Banach space
We prove that, given any ordinal $\delta < \omega_2$, there exists a transfinite $\delta$-sequence of separable Banach spaces $(X_\alpha)_{\alpha < \delta}$ such that $X_\alpha$ embeds isomorphically into $X_\beta$ and contains no subspace isomorphic to $X_\beta$ for all $\alpha < \beta < \delta$. All these spaces are subspaces of the Banach space $E_p = \bigl( \bigoplus_{n=1}^\infty \ell_p \bigr)_2$, where $1 \leq p < 2$. Moreover, assuming Martin's axiom, we prove the same for all ordinals $\delta$ of continuum cardinality.  more » « less
Award ID(s):
1700176
NSF-PAR ID:
10285954
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Carpathian Mathematical Publications
Volume:
12
Issue:
1
ISSN:
2075-9827
Page Range / eLocation ID:
88 to 93
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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