R. Mortini

activity

20082025

most citedSpectral Characteristics and Stable Ranks for the Sarason Algebra

H^{\infty} + C

11 citations · 52 across the 22 of their papers we have counts for

collaborators

26 papers

math.HO2025

Real and Complex Analysis: Solutions to Problems in Amer. Math. Monthly, Math. Magazine, College Math. J., Elemente der Math., Crux Math., EMS Newsletter, Math. Gazette

Raymond Mortini

In this arxiv-post I present my solutions (published or not) to Problems that appeared in Amer. Math. Monthly, Math. Magazine, Elemente der Mathematik and CRUX, that were mostly do…

math.CV2018

One-component inner functions II

Raymond Mortini, Joseph Cima

We continue our study of the set $I_{c}$ of inner functions $u$ in $H^{\infty}$ with the property that there is $η \in] 0, 1 [$ such that the level set $Ω_u(η):=\{z\in\mathbb D:…

math.CV2017

One-component inner functions

Joseph Cima, Raymond Mortini

We explicitely unveil several classes of inner functions $u$ in $H^{\infty}$ with the property that there is $η \in] 0, 1 [$ such that the level set $Ω_u(η):=\{z\in\mathbb D: |u(z)|<η\}…

math.FA2016

Noncoherent uniform algebras in $C^{n}$

Raymond Mortini

Let $D = D ˉ$ be the closed unit disk in $C$ and $B_{n} = B_{n} ˉ$ the closed unit ball in $C^{n}$ . For a compact subset $K$ in $\math…

math.CV2016

On the Krull Intersection Theorem in Function Algebras

Raymond Mortini, Rudolf Rupp, Amol Sasane

A version of the Krull Intersection Theorem states that for Noetherian domains, the Krull intersection $k i (I)$ of every proper ideal $I$ is trivial; that is $$ ki(I):=\displaystyle…

math.AC2016

Unitary stable ranks and norm-one ranks

Raymond Mortini

In the context of commutative $C^{*}$ -algebras we solve a problem related to a question of M. Rieffel by showing that the all-units rank and the norm-one rank coincide with the topol…

math.FA2016★ 2 cited

The covering dimension of a distinguished subset of the spectrum $M (H^{\infty})$ of $H^{\infty}$ and the algebra of real-symmetric and continuous functions on $M (H^{\infty})$

Raymond Mortini

We show that the covering dimension, $dim E$ , of the closure $E$ of the interval $] - 1, 1 [$ in the spectrum of $H^{\infty}$ equals one. Using Suárez's result that $dim M (H^{\infty}) = 2$ …

math.CV2015★ 3 cited

On a family of pseudohyperbolic disks

Raymond Mortini, Rudolf Rupp

Hyperbolic geometry plays an important role within function theory of the disk. For example, via the Schwarz-Pick Lemma, the isometries of the unit disk $D$ with respect to…

math.CV2015

A short proof of Cartan's Nullstellensatz for entire functions in $C^{n}$

Raymond Mortini

Using the fact that the maximal ideals in the polydisk algebra are given by the kernels of point evaluations, we derive a simple formula that gives a solution to the Bézout equatio…

math.FA2015★ 3 cited

Reducibility of invertible tuples to the principal component in commutative Banach algebras

Raymond Mortini, Rudolf Rupp

Let $A$ be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Suárez…

math.RA2015

The cone and cylinder algebra

Raymond Mortini, Rudolf Rupp

In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determinati…

math.CV2015

Some curiosities of the algebra of bounded Dirichlet series

Raymond Mortini, Amol Sasane

It is shown that the algebra of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that the alge…

math.FA2014★ 6 cited

Partial regularity and t-analytic sets for Banach function algebras

Joel Feinstein, Raymond Mortini

In this note we introduce the notion of $t$ -analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems rel…

math.FA2014★ 4 cited

Logarithms and exponentials in Banach algebras

Raymond Mortini, Rudolf Rupp

Let $A$ be a complex Banach algebra. If the spectrum of an invertible element $a \in A$ does not separate the plane, then $a$ admits a logarithm. We present two elementary proofs of…

math.CV2014

Holomorphic injective extensions of functions in P(K) and algebra generators

Raymond Mortini

We present necessary and sufficient conditions on planar compacta $K$ and continuous functions $f$ on $K$ in order that $f$ generates the algebras $P (K), R (K), A (K)$ or $C (K)$ . We…

math.CV2014

Embedding polydisk algebras into the disk algebra and an application to stable ranks

Raymond Mortini

It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra $A (D)$ . As a consequence, one obtains uniform closed subalgebras…

math.RA2014

The Bass and topological stable ranks of the Bohl algebra are infinite

Raymond Mortini, Rudolf Rupp, Amol Sasane

The Bohl algebra $B$ is the ring of linear combinations of functions $t^{k} e^{λ t}$ , where $k$ is any nonnegative integer, and $λ$ is any complex number, with pointwise oper…

math.RA2014

The ring of real-valued multivariate polynomials: an analyst's perspective

Raymond Mortini, Rudolf Rupp

In this survey we determine an explicit set of generators of the maximal ideals in the ring $R [x_{1}, \dots, x_{n}]$ of polynomials in $n$ variables with real coefficients and gi…

math.FA2014

The Bass and topological stable ranks for algebras of almost periodic functions on the real line

Raymond Mortini, Rudolf Rupp

Let $Λ$ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras $AP_{Λ} = {f \in AP : σ (f) \subseteq Λ}$ of almost periodic funct…

math.CV2013

Noncoherence of some rings of holomorphic functions in several variables as an easy consequence of the one-variable case

Raymond Mortini, Amol Sasane

Using the facts that the disk algebra and the Wiener algebra are not coherent, we prove that the polydisc algebra, the ball algebra and the Wiener algebra of the polydisc are not c…

math.CV2013

Corona-type theorems and division in some function algebras on planar domains

Raymond Mortini, Rudolf Rupp

Let $A$ be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if $f, f_{1}, \dots, f_{n} \in A$ satisfy $|f|\leq \sum_{j=…

math.CV2009★ 5 cited

Topological Stable Rank of $H^{\infty} (Ω)$ for Circular Domains $Ω$

Raymond Mortini, Rudolf Rupp, Amol Sasane +1

Let $Ω$ be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by $H^{\infty} (Ω)$ the Banach algebra of all bounded holomorphic function…

math.CV2009★ 11 cited

Spectral Characteristics and Stable Ranks for the Sarason Algebra $H^{\infty} + C$

Raymond Mortini, Brett D. Wick

We prove a Corona type theorem with bounds for the Sarason algebra $H^{\infty} + C$ and determine its spectral characteristics. We also determine the Bass, the dense, and the topologic…

math.CV2008★ 5 cited

Simultaneous Stabilization in $A_{R} (D)$

Raymond Mortini, Brett D. Wick

In this note we study the problem of simultaneous stabilization for the algebra $A_\R(\D)$. Invertible pairs $(f_{j}, g_{j})$ , $j = 1, ..., n$ , in a commutative unital algebra are called \…

Real and Complex Analysis: Solutions to Problems in Amer. Math. Monthly, Math. Magazine, College Math. J., Elemente der Math., Crux Math., EMS Newsletter, Math. Gazette

One-component inner functions II

One-component inner functions

Noncoherent uniform algebras in Cn

On the Krull Intersection Theorem in Function Algebras

Unitary stable ranks and norm-one ranks

The covering dimension of a distinguished subset of the spectrum M(H∞) of H∞ and the algebra of real-symmetric and continuous functions on M(H∞)

On a family of pseudohyperbolic disks

A short proof of Cartan's Nullstellensatz for entire functions in Cn

Reducibility of invertible tuples to the principal component in commutative Banach algebras

The cone and cylinder algebra

Some curiosities of the algebra of bounded Dirichlet series

Partial regularity and t-analytic sets for Banach function algebras

Logarithms and exponentials in Banach algebras

Holomorphic injective extensions of functions in P(K) and algebra generators

Embedding polydisk algebras into the disk algebra and an application to stable ranks

The Bass and topological stable ranks of the Bohl algebra are infinite

The ring of real-valued multivariate polynomials: an analyst's perspective

The Bass and topological stable ranks for algebras of almost periodic functions on the real line

Noncoherence of some rings of holomorphic functions in several variables as an easy consequence of the one-variable case

Corona-type theorems and division in some function algebras on planar domains

Topological Stable Rank of H∞(Ω) for Circular Domains Ω

Spectral Characteristics and Stable Ranks for the Sarason Algebra H∞+C

Simultaneous Stabilization in AR​(D)

Noncoherent uniform algebras in $C^{n}$

The covering dimension of a distinguished subset of the spectrum $M (H^{\infty})$ of $H^{\infty}$ and the algebra of real-symmetric and continuous functions on $M (H^{\infty})$

A short proof of Cartan's Nullstellensatz for entire functions in $C^{n}$

Topological Stable Rank of $H^{\infty} (Ω)$ for Circular Domains $Ω$

Spectral Characteristics and Stable Ranks for the Sarason Algebra $H^{\infty} + C$

Simultaneous Stabilization in $A_{R} (D)$