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
Théorèmes de structure sur certaines algèbres m-convexes commutatives.
Nous donnons dans ce travail une caractérisation des algèbres (semi-simples) localement-convexes complètes faiblement topologisées au sens de S. Warner, ce qui clarifie, entre autres, plusiers résultats données sur certaines classes d'algèbres à base étudiées par de nombreux auteurs ([2], [6], [7]) pour approcher le problème de E. A. Michael sur la continuité des caractères dans les algèbres de Fréchet [9].
Théorèmes de structures de certaines algèbres, et continuité des caractères
Topological algebras in which all maximal two-sided ideals are closed
We characterize unital topological algebras in which all maximal two-sided ideals are closed.
Topological Algebras of Functions of Bounded Variation II.
Topological algebras of kernels.
Topological algebras of random elements
Let L₀(Ω;A) be the Fréchet space of Bochner-measurable random variables with values in a unital complex Banach algebra A. We study L₀(Ω;A) as a topological algebra, investigating the notion of spectrum in L₀(Ω;A), the Jacobson radical, ideals, hulls and kernels. Several results on automatic continuity of homomorphisms are developed, including versions of well-known theorems of C. Rickart and B. E. Johnson.