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 socle and finite-dimensionality of a semiprime Banach algebra
The spatial flatness and injectiveness of Connes operator algebras.
The Spectral Radius Formula in Quotient Algebras.
The spectral topology in rings
The spectral topology of a ring is easily defined, has familiar applications in elementary Banach algebra theory, and appears relevant to abstract Fredholm and stable range theory.
The stability of multiplicative semigroup homomorphisms to real normed algebras, I.
The structure of a subclass of amenable Banach algebras.
The structure of L-ideals of measures algebras
The Taylor spectrum and quotient Banach spaces
The tensor algebra of power series spaces
The linear isomorphism type of the tensor algebra T(E) of Fréchet spaces and, in particular, of power series spaces is studied. While for nuclear power series spaces of infinite type it is always s, the situation for finite type power series spaces is more complicated. The linear isomorphism T(s) ≅ s can be used to define a multiplication on s which makes it a Fréchet m-algebra . This may be used to give an algebra analogue to the structure theory of s, that is, characterize Fréchet m-algebras...
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
The triple-norm extension problem: the nondegenerate complete case.
We prove that, if A is an associative algebra with two commuting involutions τ and π, if A is a τ-π-tight envelope of the Jordan Triple System T:=H(A,τ) ∩ S(A,π), and if T is nondegenerate, then every complete norm on T making the triple product continuous is equivalent to the restriction to T of an algebra norm on A.
The -function in -algebras.
Théorème de Cohen-Hewitt dans une algèbre de Jordan-Fréchet.
Théorème de Gelfand-Mazur dans les algèbres p-normées non-associatives.
Théorèmes de factorisation dans les algèbres completes de Jordan.
A generalization of a result of Cohen-Hewitt is given in the case of Jordan-Banach algebras. Some precisions of factorization are obtained.
Théorèmes de factorisation dans les algèbres normées complètes non associatives