On a theorem of Gleason, Kahane and Żelazko
On certain class of non-removable ideals in Banach algebras
On domination and separation of ideals in commutative Banach algebras
On domination problem in Banach algebras
On functional representation of locally -pseudoconvex algebras.
On joint spectral radii in locally convex algebras
We present several notions of joint spectral radius of mutually commuting elements of a locally convex algebra and prove that all of them yield the same value in case the algebra is pseudo-complete. This generalizes a result proved by the author in 1993 for elements of a Banach algebra.
On Liouville F-Algebras
On locally m-convex algebras of type ES
On locally pseudoconvexes square algebras.
Let A be an algebra over the field of complex numbers with a (Hausdorff) topology given by a family Q = {qλ|λ ∈ Λ} of square preserving rλ-homogeneous seminorms (rλ ∈ (0, 1]). We shall show that (A, T(Q)) is a locally m-convex algebra. Furthermore we shall show that A is commutative.
On permanent radicals in commutative locally convex algebras
On permanently singular elements in commutative m-convex locally convex algebras
On tempered integrals and derivatives of non-negative orders
On the analytic transform of bounded linear functionals on certain Banach algebras
On the ideal structure of algebras of LMC-algebra valued functions
Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.
On the joint spectral radius
We prove the -spectral radius formula for n-tuples of commuting Banach algebra elements
On the non-existence of norms for some algebras of functions
Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for where ℝ is the reals.
On The Symmetric Quaternionic Banach Algebras, I (Geljfand Theory)
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...
On topological algebra sheaves of a nuclear type
On topologically nilpotent algebras