Quasi-Banach algebras, ideals, and holomorphic functional calculus
Quasi-covariant repesentations of nuclear ...-algebras
Quasi-invariant subspaces generated by polynomials with nonzero leading terms
We introduce a partial order relation in the Fock space. Applying it we show that for the quasi-invariant subspace [p] generated by a polynomial p with nonzero leading term, a quasi-invariant subspace M is similar to [p] if and only if there exists a polynomial q with the same leading term as p such that M = [q].
Quasi-multipliers of the algebra of approximable operators and its duals
Let A be the Banach algebra of approximable operators on an arbitrary Banach space X. For the spaces of all bilinear continuous quasi-multipliers of A resp. its dual A* resp. its bidual A**, concrete representations as spaces of operators are given.
Quasimultipliers on -algebras.
Quelques propriétés des éléments et fonctions analytiques au sens de Krasner
Quotient Banach spaces
Quotient Banach spaces; Multilinear theory
Range inclusion results for derivations on noncommutative Banach algebras
Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes a result...
Rank and the Drazin inverse in Banach algebras
Let A be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of A. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of A.
Rank one elements in Banach algebras
Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems
As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.
Rapport sur le prolongement analytique dans les corps values complets par la méthode des éléments analytiques quasi-connexes
Real Banach Algebras. II.
Real Gelfand-Mazur algebras.
Real Gel'fand-Mazur division algebras.
Recent trends in the field of Jordan-Banach algebras
Reciprocity theorems in the theory of representations of groups and algebras [Book]
Reductive Algebras with Minimal Ideals.
Regular quasimultipliers of some semisimple Banach algebras