A new extension of Komlós' theorem in infinite dimensions. Application: Weak compactness in .
Saadoune, M. (1998)
Portugaliae Mathematica
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Saadoune, M. (1998)
Portugaliae Mathematica
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Matsumoto, Toshiko, Watanabe, Seiji (2000)
International Journal of Mathematics and Mathematical Sciences
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B. Johnson (1997)
Studia Mathematica
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Bade, Curtis and Dales have introduced the idea of weak amenability. A commutative Banach algebra A is weakly amenable if there are no non-zero continuous derivations from A to A*. We extend this by defining an alternating n-derivation to be an alternating n-linear map from A to A* which is a derivation in each of its variables. Then we say that A is n-dimensionally weakly amenable if there are no non-zero continuous alternating n-derivations on A. Alternating n-derivations are the same...
Kinnunen, Juha, Martio, Olli (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Agarwal, Ravi P., O'Regan, Donal, Liu, Xinzhi (2005)
Fixed Point Theory and Applications [electronic only]
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Cheung, Wing-Sum (2001)
International Journal of Mathematics and Mathematical Sciences
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H. Dales, F. Ghahramani, N. Grønbæek (1998)
Studia Mathematica
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We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space is zero; i.e., . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable;...
Jiří Vala (1999)
Applications of Mathematics
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The aim of this paper is to demonstrate how the variational equations from can be formulated and solved in some abstract Banach spaces without any a priori construction of special linearization schemes. This should be useful e.g. in the analysis of heat conduction problems and modelling of flow in porous media.
Charles Dunkl, Donald Ramirez (1973)
Studia Mathematica
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