On the fundamental inequality in locally multiplicatively convex algebras
On the radical in Hermitian LMC algebras
On the spectral properties of elements of the type exp(ih) in Hermitian Banach algebras
On the spectral radius in locally multiplicatively convex topological algebras
On the uniform boundedness of elements of the type in Hermitian lmc-algebras
On the uniqueness of uniform norms and C*-norms
We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm; this is...
Prehermitian Elements and B*-Algebras.
Pure States and P-Commutative Banach *-Algebras.
Quasi *-algebras of measurable operators
Non-commutative -spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p ≥ 2 they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. CQ*-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (,₀) with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra...
Range-commutativity maps on *-algebras.
Regular operators on partial inner product spaces
Representational indices of derivations of C*-algebras and representations of *-algebras on Krein spaces.
*-Representations, seminorms and structure properties of normed quasi *-algebras
The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity...
Sesquilinear and Quadratic Forms on Modules Over *-algebras
Some remarks about the three spaces problem in Banach algebras
Some seminorms on quasi *-algebras
Different types of seminorms on a quasi *-algebra (𝔄,𝔄₀) are constructed from a suitable family ℱ of sesquilinear forms on 𝔄. Two particular classes, extended C*-seminorms and CQ*-seminorms, are studied in some detail. A necessary and sufficient condition for the admissibility of a sesquilinear form in terms of extended C*-seminorms on (𝔄,𝔄₀) is given.
Spatiality of derivations of Fréchet GB*-algebras
We show that every continuous derivation of a countably dominated Fréchet GB*-algebra A is spatial whenever A is additionally an AO*-algebra.
Sur la continuité automatique des épimorphismes dans les -algèbres de Banach.
Sur un problème de I. Glicksberg : les idéaux fermés de type fini de
Soit , algèbre de convolution des mesures de Radon bornées sur le groupe abélien localement compact . Pour que soit fermé dans (ou, ce qui revient au même, pour que soit fermé), il faut et il suffit que soit la convolution d’une mesure inversible et d’une mesure idempotente.
Survey of some results in spectral theory obtained in Prague