# A class of $$\ell ^p$$ ℓ p saturated Banach spaces

A class of $$\ell ^p$$ ℓ p saturated Banach spaces We present a new class of reflexive $$\ell ^p$$ ℓ p saturated Banach spaces $$\mathfrak{X }_p$$ X p for $$1<p<\infty$$ 1 < p < ∞ with rather tight structure. The norms of these spaces are defined with the use of a modification of the standard method yielding hereditarily indecomposable Banach spaces. The space $$\mathfrak{X }_p$$ X p does not embed into a space with an unconditional basis and for any analytic decomposition into two subspaces, it is proved that one of them embeds isomorphically into the $$\ell ^p$$ ℓ p -sum of a sequence of finite dimensional normed spaces. We also study the space of operators of $$\mathfrak{X }_p$$ X p . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# A class of $$\ell ^p$$ ℓ p saturated Banach spaces

, Volume 18 (2) – Jun 14, 2013
31 pages

/lp/springer_journal/a-class-of-ell-p-p-saturated-banach-spaces-m0yllrpNvo
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0245-5
Publisher site
See Article on Publisher Site

### Abstract

We present a new class of reflexive $$\ell ^p$$ ℓ p saturated Banach spaces $$\mathfrak{X }_p$$ X p for $$1<p<\infty$$ 1 < p < ∞ with rather tight structure. The norms of these spaces are defined with the use of a modification of the standard method yielding hereditarily indecomposable Banach spaces. The space $$\mathfrak{X }_p$$ X p does not embed into a space with an unconditional basis and for any analytic decomposition into two subspaces, it is proved that one of them embeds isomorphically into the $$\ell ^p$$ ℓ p -sum of a sequence of finite dimensional normed spaces. We also study the space of operators of $$\mathfrak{X }_p$$ X p .

### Journal

PositivitySpringer Journals

Published: Jun 14, 2013

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