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 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 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 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 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 lattice of precompact topologies on .
The Norm-Strict Bidual of a Banach Algebra and the Dual of Cu(G).
The Relative Spectrum of Elements in a Real Banach Algebra.
The second conjugate algebras of Banach algebras.
The Shirali-Ford theorem as a consequence of Ptak theory for hermitian Banach algebras
A simple application of Pták theory for hermitian Banach algebras, combined with a result on normed Q-algebras, gives a non-technical new proof of the Shirali-Ford theorem. A version of this theorem in the setting of non-normed topological algebras is also provided.
The stability of multiplicative semigroup homomorphisms to real normed algebras, I.
The three-space-problem for locally-m-convex algebras.
We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.
The trace of finite and nuclear elements in Banach algebras