Displaying similar documents to “Weak * -continuous derivations in dual Banach algebras”

A note on fusion Banach frames

S. K. Kaushik, Varinder Kumar (2010)

Archivum Mathematicum

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For a fusion Banach frame ( { G n , v n } , S ) for a Banach space E , if ( { v n * ( E * ) , v n * } , T ) is a fusion Banach frame for E * , then ( { G n , v n } , S ; { v n * ( E * ) , v n * } , T ) is called a fusion bi-Banach frame for E . It is proved that if E has an atomic decomposition, then E also has a fusion bi-Banach frame. Also, a sufficient condition for the existence of a fusion bi-Banach frame is given. Finally, a characterization of fusion bi-Banach frames is given.

On the Lipschitz operator algebras

A. Ebadian, A. A. Shokri (2009)

Archivum Mathematicum

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In a recent paper by H. X. Cao, J. H. Zhang and Z. B. Xu an α -Lipschitz operator from a compact metric space into a Banach space A is defined and characterized in a natural way in the sence that F : K → A is a α -Lipschitz operator if and only if for each σ ∈ X * the mapping σ ∘ F is a α -Lipschitz function. The Lipschitz operators algebras L α ( K , A ) and l α ( K , A ) are developed here further, and we study their amenability and weak amenability of these algebras. Moreover, we prove an interesting result that L α ( K , A ) and l α ( K , A ) are...

A converse to Amir-Lindenstrauss theorem in complex Banach spaces.

Ondrej F. K. Kalenda (2006)

RACSAM

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We show that a complex Banach space is weakly Lindelöf determined if and only if the dual unit ball of any equivalent norm is weak* Valdivia compactum. We deduce that a complex Banach space X is weakly Lindelöf determined if and only if any nonseparable Banach space isomorphic to a complemented subspace of X admits a projectional resolution of the identity. These results complete the previous ones on real spaces.