On some inequalities in normed algebras.
On Some Properties of Segal Algebras and Their Multipliers.
On spectral continuity of positive elements
Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the...
On splitting of extensions of rings and topological rings.
On the Barrelledness of a topological Algebra Relative to its Spectrum
On the circle-exponent function
On the fundamental inequality in locally multiplicatively convex 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 radii of commuting Banach algebra elements
Some inequalities are proved between the geometric joint spectral radius (cf. [3]) and the joint spectral radius as defined in [7] of finite commuting families of Banach algebra elements.
On the joint spectral radius
We prove the -spectral radius formula for n-tuples of commuting Banach algebra elements
On the largest generalized joint spectrum
On the left and right joint spectra in Banach algebras
On the locally -convex algebra and a differential-geometric interpretation of it.
On the punctured neighbourhood theorem.
On the radical in Hermitian LMC algebras
On the ranks of Elements of Semiprime Banach Algebras
On the spectra of elements in certain algebras of vector valued functions and sequences.
On the spectral radius in locally multiplicatively convex topological algebras
On the structure of rank one elements in Banach algebras.
On the ultrametric Stone-Weierstrass theorem and Mahler's expansion
We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If is a subset of a rank-one valuation domain , we show that the ring of polynomial functions is dense in the ring of continuous functions from to if and only if the topological closure of in the completion of is compact. We then show how to expand continuous functions in sums of polynomials.