Displaying similar documents to “Complemented copies of ℓ p spaces in tensor products”

Invariant subspaces of X * * under the action of biconjugates

Sophie Grivaux, Jan Rychtář (2006)

Czechoslovak Mathematical Journal

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We study conditions on an infinite dimensional separable Banach space X implying that X is the only non-trivial invariant subspace of X * * under the action of the algebra 𝔸 ( X ) of biconjugates of bounded operators on X : 𝔸 ( X ) = { T * * T ∈ ℬ ( X ) } . Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of c 0 , and show in particular that any space which does not contain ℓ 1 and has property (u) of Pelczynski is simple.

Oscillation of a nonlinear difference equation with several delays

X. N. Luo, Yong Zhou, C. F. Li (2003)

Mathematica Bohemica

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In this paper we consider the nonlinear difference equation with several delays ( a x n + 1 + b x n ) k - ( c x n ) k + ∑ i = 1 m p i ( n ) x n - σ i k = 0 where a , b , c ∈ ( 0 , ∞ ) , k = q / r , q , r are positive odd integers, m , σ i are positive integers, { p i ( n ) } , i = 1 , 2 , ⋯ , m , is a real sequence with p i ( n ) ≥ 0 for all large n , and lim inf n → ∞ p i ( n ) = p i < ∞ , i = 1 , 2 , ⋯ , m . Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.

Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures

Giovanni Emmanuele (1996)

Commentationes Mathematicae Universitatis Carolinae

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In the paper [5] L. Drewnowski and the author proved that if X is a Banach space containing a copy of c 0 then L 1 ( μ , X ) is complemented in c a b v ( μ , X ) and conjectured that the same result is true if X is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if μ is a finite measure and X is a Banach lattice not containing copies of c 0 , then L 1 ( μ , X ) is complemented in c a b v ( μ , X ) . Here, we show that the complementability of L 1 ( μ , X ) ...