Displaying similar documents to “A note on a construction of J. F. Feinstein”

Higher-dimensional weak amenability

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...

Derivations into iterated duals of Banach algebras

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 A ( n ) is zero; i.e., ℋ 1 ( A , A ( n ) ) = 0 . 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;...

Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

Fabian, Marián, Hájek, Petr, Zizler, Václav (1997)

Serdica Mathematical Journal

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* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada). It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly...

Swiss cheeses, rational approximation and universal plane curves

J. F. Feinstein, M. J. Heath (2010)

Studia Mathematica

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We consider the compact plane sets known as Swiss cheese sets, which are a useful source of examples in the theory of uniform algebras and rational approximation. We develop a theory of allocation maps connected to such sets and we use this theory to modify examples previously constructed in the literature to obtain examples homeomorphic to the Sierpiński carpet. Our techniques also allow us to avoid certain technical difficulties in the literature.

Uniformly counting rational points on conics

Efthymios Sofos (2014)

Acta Arithmetica

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We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over ℚ. The estimate is uniform in the coefficients of the underlying quadratic form.

Rational Constants of Generic LV Derivations and of Monomial Derivations

Janusz Zieliński (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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We describe the fields of rational constants of generic four-variable Lotka-Volterra derivations. Thus, we determine all rational first integrals of the corresponding systems of differential equations. Such systems play a role in population biology, laser physics and plasma physics. They are also an important part of derivation theory, since they are factorizable derivations. Moreover, we determine the fields of rational constants of a class of monomial derivations.

Banach space properties of strongly tight uniform algebras

Scott Saccone (1995)

Studia Mathematica

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We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K),...

Amenability and the second dual of a Banach algebra

Frédéric Gourdeau (1997)

Studia Mathematica

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Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.

Booleanization of uniform frames

Bernhard Banaschewski, Aleš Pultr (1996)

Commentationes Mathematicae Universitatis Carolinae

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Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.