# The complete continuity properties for the positive projective tensor product of atomic Banach lattices

The complete continuity properties for the positive projective tensor product of atomic Banach... Let E be an atomic Banach lattice and X be a separable Banach lattice. In this paper we show that $${E \hat{\otimes}_{|\pi|} X,}$$ the positive projective tensor product of E and X, has the complete continuity property (respectively, the analytic complete continuity property) if and only if both E and X have the same property. We also discuss the inheritance of type I- and type II-complete continuity properties by $${E \hat{\otimes}_{|\pi|} X}$$ from E and X. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# The complete continuity properties for the positive projective tensor product of atomic Banach lattices

, Volume 17 (1) – Sep 16, 2011
9 pages

/lp/springer_journal/the-complete-continuity-properties-for-the-positive-projective-tensor-BiGmGOSqcz
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/s11117-011-0141-9
Publisher site
See Article on Publisher Site

### Abstract

Let E be an atomic Banach lattice and X be a separable Banach lattice. In this paper we show that $${E \hat{\otimes}_{|\pi|} X,}$$ the positive projective tensor product of E and X, has the complete continuity property (respectively, the analytic complete continuity property) if and only if both E and X have the same property. We also discuss the inheritance of type I- and type II-complete continuity properties by $${E \hat{\otimes}_{|\pi|} X}$$ from E and X.

### Journal

PositivitySpringer Journals

Published: Sep 16, 2011

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