Related papers: Quasianalyticity in certain Banach function algebr…
We provide a survey of the similarities and differences between Banach and Frechet algebras including some known results and examples. We also collect some important generalizations in abstract harmonic analysis; for example, the…
In this paper, we study the notion of $\phi$-biflatness, $\phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples…
Given a Banach space $A$ and fix a non-zero $\varphi\in A^*$ with $\|\varphi\|\leq 1$. Then the product $a\cdot b=\langle\varphi, a\rangle\ b$ turning $A$ into a Banach algebra which will be denoted by $_\varphi A.$ Some of the main…
Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…
Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain…
We prove two main results on Denjoy-Carleman classes: (1) a composite function theorem which asserts that a function f(x) in a quasianalytic Denjoy-Carleman class Q, which is formally composite with a generically submersive mapping y=h(x)…
We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…
We refine a construction of Choi, Farah and Ozawa to build a nonseparable amenable operator algebra $\mathcal A\subseteq\ell_\infty(M_2)$ whose nonseparable subalgebras, including $\mathcal A$, are not isomorphic to a $C^*$-algebra. This is…
A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to…
Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for \emph{approximate} amenability have been open for some years now. In this article we give a complete…
We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces.…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in non-Archimedean…
By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group $\mathbb{G}$ a completely contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a deformed Fourier…
The purpose of this paper is to define semi- and subanalytic subsets and maps in the context of real analytic orbifolds and to study their basic properties. We prove results analogous to some well-known results in the manifold case. For…
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…
A study is made, of families of Hamiltonians parameterized over open subsets of Banach spaces in a way which renders many interesting properties of eigenstates and thermal states analytic functions of the parameter. Examples of such…
In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.
Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators.…
Let $A$ be a unital Banach function algebra with character space $\Phi_A$. For $x\in \Phi_A$, let $M_x$ and $J_x$ be the ideals of functions vanishing at $x$, and in a neighbourhood of $x$, respectively. It is shown that the hull of $J_x$…
We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A. This extends a recent result by Dominguez who has dealt…