相关论文: A Peak Point Theorem for Uniform Algebras on Real-…

It is shown that there exists a normal uniform algebra, on a compact metrizable space, that fails to be strongly regular at some peak point. This answers a 31-year-old question of Joel Feinstein. Our example is R(K) for a certain compact…

It is shown that if $A$ is a uniform algebra generated by real-analytic functions on a suitable compact subset $K$ of a real-analytic variety such that the maximal ideal space of $A$ is $K$, and every continuous function on $K$ is locally a…

A survey is given of the work on strong regularity for uniform algebras over the last thirty years, and some new results are proved, including the following. Let A be a uniform algebra on a compact space X and let E be the set of all those…

We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if $X$ is a perfectly normal space which can be covered by a disjoint…

Using the variational method, it is shown that the set of all strong peak functions in a closed algebra $A$ of $C_b(K)$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we can induce the…

We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by…

We strengthen, in various directions, the theorem of Garnett that every $\sigma$-compact, completely regular space $X$ occurs as a Gleason part for some uniform algebra. In particular, we show that the uniform algebra can always be chosen…

Nous montrons qu'un raffinement du th\'eor\`eme de Siegel sur les points entiers de courbes alg\'ebriques impliquerait la conjecture abc de Masser-Oesterl\'e. Nous formulons une hypoth\`ese "Siegel uniforme" qui est une majoration de la…

It is shown that there exists a nontrivial uniform algebra that is Dirichlet on its maximal ideal space and has a dense set of elements that are exponentials. This answers a 65-year-old question of John Wermer and a 17-year-old question of…

Let $X$ be a general complex projective hypersurface in $\mathbb{P}^{n+1}$ of degree $d>1$. A point $P$ not in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group. We prove…

In this paper, we equip a C*-algebra-valued b-metric spaces with a graph G = (V,E) and establish some common fixed point theorems. Also, some examples in support of our main results are provided. Finally, as applications, existence and…

Let X be a compact Hausdorf space, let A be a commutative unital Banach algebra, and let C(X,A) denote the algebra of continuous A-valued functions on $X$ equipped with the uniform norm ||f||=sup{||f(x)||:x\in X} for all f in C(X,A).…

The closed one-sided ideals of a C*-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C*-algebra B which contains the unit…

We give a survey of the known connections between regularity conditions and amenability conditions in the setting of uniform algebras. For a uniform algebra $A$ we consider the set, $A_{lc}$, of functions in $A$ which are locally constant…

Let $Z$ be a projective geometrically integral algebraic variety. This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. The bounds obtained are uniform in varieties of fixed degree and…

A well-known result says that the Euclidean unit ball is the unique fixed point of the polarity operator. This result implies that if, in $\mathbb{R}^n$, the unit ball of some norm is equal to the unit ball of the dual norm, then the norm…

The peak algebra is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks. By exploiting the combinatorics of sparse subsets of [n-1] (and of certain classes of compositions…

For a finitely aligned k-graph $\Lambda$ with X a set of vertices in $\Lambda$ we define a universal C*-algebra called $C^*(\Lambda,X)$ generated by partial isometries. We show that $C^*(\Lambda,X)$ is isomorphic to the corner…

Let X be an analytic vector field on a real or complex 2-manifold, and K a compact set of zeros of X whose fixed point index is not zero. Let A denote the Lie algebra of analytic vector fields Y on M such that at every point of M the values…

Brouwer's fixed point theorem states that any continuous function from a closed $n$-dimensional ball to itself has a fixed point. In 1961, Klee showed that if such a function has discontinuities that are bounded, then it has a point that is…