On topologically nilpotent algebras
On topologizable algebras
On Uniform Continuity of the Spectral Radius in Banach Algebras.
On uniformly continuous operators and some weight-hyperbolic function Banach algebra.
On weakly compact operators from some uniform algebras
On z◦ -ideals in C(X)
An ideal I in a commutative ring R is called a z°-ideal if I consists of zero divisors and for each a ∈ I the intersection of all minimal prime ideals containing a is contained in I. We characterize topological spaces X for which z-ideals and z°-ideals coincide in , or equivalently, the sum of any two ideals consisting entirely of zero divisors consists entirely of zero divisors. Basically disconnected spaces, extremally disconnected and P-spaces are characterized in terms of z°-ideals. Finally,...
On Α Bochner΄s Type Theorem in Topological Algebras
Operators determining the complete norm topology of C(K)
For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and , we show that every complete norm on A which makes continuous the multiplication by is equivalent to provided that has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).
Operators on some function spaces
Operator-valued analytic functions of constant norm
Optimal Quadrature of Hp Functions.
Outer and inner vanishing measures and division in H∞ + C.
Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in H∞ + C. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in H∞ + C.
Outers for noncommutative revisited
We continue our study of outer elements of the noncommutative spaces associated with Arveson’s subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in actually satisfy the stronger condition that there exist aₙ ∈ A with haₙ ∈ Ball(A)...
Partitions of spectral sets
P-commutativity of the Banach Algebra L1 (G).
Peak Points for Algebras on Circled Sets.
Pervasive algebras and maximal subalgebras
A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X). It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive...
Pervasive algebras on planar compacts
We characterize compact sets in the Riemann sphere not separating for which the algebra of all functions continuous on and holomorphic on , restricted to the set , is pervasive on .
Picard's theorem, Mittag-Leffler methods, and continuity of characters on Fréchet algebras
Pick interpolation for a uniform algebra