# Geometrical properties of Banach spaces generated by sublinear operators

Geometrical properties of Banach spaces generated by sublinear operators We solve a problem posed by Mastylo (Math Japon 36(1), 85–92, 1991) proving that every “non-trivial” subspace of a Banach space X generated by some positive sublinear operator and an L p -space with 1 ≤  p < ∞ contains, for any $${\varepsilon > 0}$$ , an $${(1 + \varepsilon)}$$ -copy of l p which is $${(1 + \varepsilon)}$$ -complemented in X. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Geometrical properties of Banach spaces generated by sublinear operators

, Volume 17 (2) – Feb 12, 2012
12 pages

/lp/springer_journal/geometrical-properties-of-banach-spaces-generated-by-sublinear-66Pm0yZDCo
Publisher
SP Birkhäuser Verlag Basel
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/s11117-012-0159-7
Publisher site
See Article on Publisher Site

### Abstract

We solve a problem posed by Mastylo (Math Japon 36(1), 85–92, 1991) proving that every “non-trivial” subspace of a Banach space X generated by some positive sublinear operator and an L p -space with 1 ≤  p < ∞ contains, for any $${\varepsilon > 0}$$ , an $${(1 + \varepsilon)}$$ -copy of l p which is $${(1 + \varepsilon)}$$ -complemented in X.

### Journal

PositivitySpringer Journals

Published: Feb 12, 2012

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