Tensor products of topological algebras and analytic sets
The beginning of the spectral theory of Nevanlinna's mapping from topological space to endomorphisms algebra of Banach space and its applications.
The -algebra of a Hilbert bimodule
Un -modulo hilbertiano destro su una -algebra dotato di uno -omomorfismo isometrico viene qui considerato come un oggetto della -categoria degli -moduli Hilbertiani destri. Come in [11], associamo ad esso una -algebra contenente come un «-bimodulo hilbertiano in ». Se è pieno e proiettivo finito è la -algebra , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, è canonicamente immersa...
The canonical test case for the non-commutative Singer-Wermer conjecture
It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer originally raised the question in 1955 for the case of commutative Banach algebras, the conjecture is...
The center of topologically primitive exponentially galbed algebras.
The center of topologically primitive galbed algebras
It is shown that every unital σ-complete topologically primitive strongly galbed Hausdorff algebra in which all elements are bounded is central
The centroid of a JB*-triple system.
The characteristic algebra of a polynomial covering map.
The closure of the invertibles in a von Neumann algebra
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman...
The compactum and finite dimensionality in Banach algebras.
The continuity of Lie homomorphisms
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
The Gleason-Kahane-Zelazko theorem and function algebras
A theorem due to A. Gleason, J.-P. Kahane and W. Zelazko characterizes continuous characters within the space of all continuous linear forms of a locally multiplicatively convex, sequentially complete algebra. The present paper applies these results to investigate linear isometries of Banach algebras (with particular attention to normal uniform algebras) and of some locally multiplicatively convex algebras. The locally multiplicatively convex algebra of all holomorphic functions on a domain, will...
The Gleason-Kahane-Żelazko theorem and its generalizations
This expository article deals with results surrounding the following question: Which pairs of Banach algebras A and B have the property that every unital invertibility preserving linear map from A to B is a Jordan homomorphism?
The group of invertible elements in a Banach algebra
The holomorphic functional calculus as an operational calculus
The index for Fredholm elements in a Banach algebra via a trace
We show that the existence of a trace on an ideal in a Banach algebra provides an elegant way to develop the abstract index theory of Fredholm elements in the algebra. We prove some results on the problem of the equality of the nonzero exponential spectra of elements ab and ba and use the index theory to formulate a condition guaranteeing this equality in a quotient algebra.
The index for Fredholm elements in a Banach algebra via a trace II
We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.
The inverse spectral radius formula and removability of spectrum
The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces
A classical Julia-Carathéodory theorem concerning radial limits of holomorphic maps in one dimension is extended to hyperbolic contractions of bounded symmetric domains in J*-algebras.
The lattice of precompact topologies on .