A remark on functional continuity of certain Fréchet algebras
A spectral theory for locally compact abelian groups of automorphisms of commutative Banach algebras
Let A be a commutative Banach algebra with Gelfand space ∆ (A). Denote by Aut (A) the group of all continuous automorphisms of A. Consider a σ(A,∆(A))-continuous group representation α:G → Aut(A) of a locally compact abelian group G by automorphisms of A. For each a ∈ A and φ ∈ ∆(A), the function t ∈ G is in the space C(G) of all continuous and bounded functions on G. The weak-star spectrum is defined as a closed subset of the dual group Ĝ of G. For φ ∈ ∆(A) we define to be the union of all...
Bundles of Banach algebras.
Calcul fonctionnel holomorphe dans les algèbres de Banach ultramétriques
Doubly commuting operator representations of Dirichlet algebras
Extension of algebra norms and applications
Fuglede-type decompositions of representations
It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.
Gelfand theorem implies Stone representation theorem of Boolean rings.
Intertwining operators
On dense ideals of C*-algebras and generalizations of the Gelfand-Naimark Theorem
We develop the theory of Segal algebras of commutative C*-algebras, with an emphasis on the functional representation. Our main results extend the Gelfand-Naimark Theorem. As an application, we describe faithful principal ideals of C*-algebras. A key ingredient in our approach is the use of Nachbin algebras to generalize the Gelfand representation theory.
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.
Partitions of spectral sets
Pure quasi-states and extremal quasi-measures.
Real Banach Algebras. II.
Representation generated by a finite number of Hilbert space operators
Some absolutely continuous representations of function algebras.
Some spectral properties of operator-valued representations of function algebras
Spectral subspaces for the Fourier algebra
In this note we define and explore, à la Godement, spectral subspaces of Banach space representations of the Fourier-Eymard algebra of a (nonabelian) locally compact group.
Synthèse harmonique ultramétrique. Théorie spectrale en analyse ultramétrique
The Banach algebra of continuous bounded functions with separable support
We prove a commutative Gelfand-Naimark type theorem, by showing that the set of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...