-Topologies on the Test Function Algebra
Old and new results on Allan's GB*-algebras
This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication...
On a problem of Fell and Doran
On Banach *-algebras without the unit
On certain trigonometric sums in several variables.
On Continuity of Algebra Homomorphisms and Uniqueness of Metric Topology.
On embedding of involution rings.
On functional representation of locally -pseudoconvex algebras.
On generalized eigenfunctions of operators in a Hilbert space
On generalized right modular complemented algebras
On ideals and quotients of Hermitian algebras
On Jordan algebras of Baire type.
On Jordan *-derivations and an application
On Making Involutive vector spaces into Topological *-Algebras
On representations of partial *-algebras based on -weights.
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 behaviour of Jordan-algebra norms on associative algebras
We prove that for a suitable associative (real or complex) algebra which has many nice algebraic properties, such as being simple and having minimal idempotents, a norm can be given such that the mapping (a,b) ↦ ab + ba is jointly continuous while (a,b) ↦ ab is only separately continuous. We also prove that such a pathology cannot arise for associative simple algebras with a unit. Similar results are obtained for the so-called "norm extension problem", and the relationship between these results...
On the equivalence of Hermitian inner products on topological *-algebras.
On the existence of configurations of subspaces in a Hilbert space with fixed angles.
On the fundamental inequality in locally multiplicatively convex algebras