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Contractible quantum Arens-Michael algebras

Nina V. Volosova (2010)

Banach Center Publications

We consider quantum analogues of locally convex spaces in terms of the non-coordinate approach. We introduce the notions of a quantum Arens-Michael algebra and a quantum polynormed module, and also quantum versions of projectivity and contractibility. We prove that a quantum Arens-Michael algebra is contractible if and only if it is completely isomorphic to a Cartesian product of full matrix C*-algebras. Similar results in the framework of traditional (non-quantum) approach are established, at the...

Derivations into iterated duals of Banach algebras

H. Dales, F. Ghahramani, N. Grønbæek (1998)

Studia Mathematica

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., 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; we study...

Déterminant associé à une trace sur une algèbre de Banach

Pierre de La Harpe, Georges Skandalis (1984)

Annales de l'institut Fourier

Soient A une algèbre de Banach complexe, G L ( A ) le groupe général linéaire stable de A et G L 0 ( A ) sa composante connexe pour la topologie normique. Nous montrons que toute trace non nulle r : A C permet de définir un homomorphisme Δ r de G L 0 ( A ) sur le quotient du groupe additif C par l’image r _ ( K 0 ( A ) ) du groupe de Grothendieck de A . Si A = M n ( C ) (respectivement si A est un facteur fini continu) avec la trace usuelle, alors exp ( i 2 π Δ r ) est le déterminant usuel (resp. exp ( Re ( i 2 π Δ r ) ) est celui de Fuglede et Kadison). Dans le cas général, les déterminants Δ r permettent...

Extension of CR functions to «wedge type» domains

Andrea D'Agnolo, Piero D'Ancona, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X be a complex manifold, S a generic submanifold of X R , the real underlying manifold to X . Let Ω be an open subset of S with Ω analytic, Y a complexification of S . We first recall the notion of Ω -tuboid of X and of Y and then give a relation between; we then give the corresponding result in terms of microfunctions at the boundary. We relate the regularity at the boundary for ¯ b to the extendability of C R functions on Ω to Ω -tuboids of X . Next, if X has complex dimension 2, we give results on extension...

Higher-dimensional weak amenability

B. Johnson (1997)

Studia Mathematica

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 as alternating...

Hochschild cohomology groups of certain algebras of analytic functions with coefficients in one-dimensional bimodules

Olaf Ermert (1999)

Studia Mathematica

We compute the algebraic and continuous Hochschild cohomology groups of certain Fréchet algebras of analytic functions on a domain U in n with coefficients in one-dimensional bimodules. Among the algebras considered, we focus on A=A(U). For this algebra, our results apply if U is smoothly bounded and strictly pseudoconvex, or if U is a product domain.

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