Completely positive maps on amalgamated product C*-algebras.
Computing and estimating the global dimension in certain classes af Banach algebras.
Connes amenability-like properties
We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.
Constructions preserving -weak amenability of Banach algebras
A surjective bounded homomorphism fails to preserve -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
Contractible quantum Arens-Michael algebras
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...
Counterexample on semiradial Banach algebras
Crossed products by Hilbert pro-C*-bimodules
We define the crossed product of a pro-C*-algebra A by a Hilbert A-A pro-C*-bimodule and we show that it can be realized as an inverse limit of crossed products of C*-algebras by Hilbert C*-bimodules. We also prove that under some conditions the crossed products of two Hilbert pro-C*-bimodules over strongly Morita equivalent pro-C*-algebras are strongly Morita equivalent.
Derivations into iterated duals of Banach algebras
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; we study...
Derivations of Nest Algebras.
Determinant lines, von Neumann algebras and L2 torsion.
Diagonalization of a self-adjoint operator acting on a Hilbert module.
Direct limit of matricially Riesz normed spaces.
Direct limit of matricially Riesz normed spaces
In this paper, the -Riesz norm for ordered -bimodules is introduced and characterized in terms of order theoretic and geometric concepts. Using this notion, -Riesz normed bimodules are introduced and characterized as the inductive limits of matricially Riesz normed spaces.
Einfache Moduln über gewissen Banachschen Algebren: Ein Imprimitivitätssatz .
Extensiones finitogeneradas y proyectivas de un álgebra m-convexa.
Factorization in Fréchet spaces
Finite generation in C*-algebras and Hilbert C*-modules
We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.
Gelfand representation of Banach modules [Book]
Higher-dimensional weak amenability
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
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 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 . The so called projective operator tensor product of two operator modules X and Y over an abelian von Neumann algebra C is introduced...