Harmonic analysis of Abelian inner automorphism groups of von Neumann algebras.
Induced bornological representations of bornological algebras
Interpolation et idéaux de fonctions analytiques bornées
Multiplier algebras, Banach bundles, and one-parameter semigroups
Nilpotente Liesche Gruppen haben symmetrische Gruppenalgebren.
Noncommutative uniform algebras
We show that a real Banach algebra A such that ||a²|| = ||a||² for a ∈ A is a subalgebra of the algebra of continuous quaternion-valued functions on a compact set X.
Non-Replaceable Matrices.
On a problem of Fell and Doran
On Cohen's proof of the Factorization Theorem
Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
On functional representation of locally -pseudoconvex algebras.
On Representations in Banach Spaces.
On the algebra of smooth operators
Let s be the space of rapidly decreasing sequences. We give the spectral representation of normal elements in the Fréchet algebra L(s',s) of so-called smooth operators. We also characterize closed commutative *-subalgebras of L(s',s) and establish a Hölder continuous functional calculus in this algebra. The key tool is the property (DN) of s.
On the categories and . II
On topological algebra sheaves of a nuclear type
Partially defined σ-derivations on semisimple Banach algebras
Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation...
Partitions of the Spectrum of a Topological Algebra through Geometric hulls
Perturbation theorems for Hermitian elements in Banach algebras
Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
Polynomially compact derivations on Banach algebras
We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.
Pseudo-Banach algebras
Quasi-covariant repesentations of nuclear ...-algebras