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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...

Hilbert modules and tensor products of operator spaces

Bojan Magajna (1997)

Banach Center Publications

The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H ¯ ⨂ ^ H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C*-algebra is shown to be completely bounded with ∥ b ∥ c b = ∥ b ∥ . The so called projective operator tensor product of two operator modules X and Y over an abelian von Neumann algebra C is introduced...

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 ℂ 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.

Homological dimensions and approximate contractibility for Köthe algebras

Alexei Yu. Pirkovskii (2010)

Banach Center Publications

We give a survey of our recent results on homological properties of Köthe algebras, with an emphasis on biprojectivity, biflatness, and homological dimension. Some new results on the approximate contractibility of Köthe algebras are also presented.

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