Antonio Acuaviva

activity

20212026

most citedFactorizations and minimality of the Calkin Algebra norm for

C (K)

-spaces

1 citations · 2 across the 19 of their papers we have counts for

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15 papers · 1 filter

math.FA2026

A negative solution to the complemented subspace problem for Banach spaces with unconditional bases

Antonio Acuaviva

We give a negative solution to the complemented subspace problem for Banach spaces with unconditional bases over both the real and complex fields. For every $ρ > 0$ , we construct a p…

math.FA2026

Banach's Isometric Conjecture over the Complex Field

Antonio Acuaviva, Tomasz Kania

We complete Banach's isometric conjecture over the complex field. More precisely, if $X$ is a complex normed space and, for some $2\leqslant n<\dim_{\C}X$, all its $n$-dimens…

math.FA2026

Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory

Antonio Acuaviva, Pablo Acuaviva

We investigate the capacity of current language models to contribute to mathematical research. In Banach space theory, AI systems generated key ideas and proofs for five new result…

math.FA2026

A Unital Banach Algebra Which Is Not a Calkin Algebra

Antonio Acuaviva, Pablo Acuaviva

Let $A (X)$ and $K (X)$ denote the ideals of approximable and compact operators on a Banach space $X$ , respectively. We construct a unital Banach algebra $A$ of d…

math.FA2026

A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual

Antonio Acuaviva

We construct a separable Banach space $X$ with a Schauder basis such that $B_{X}$ is not a uniformly continuous retract of $B_{X^{**}}$ . Consequently, $X$ is not a uniformly continuo…

math.FA2026

Pure infiniteness and primary factorisation

Antonio Acuaviva, Bence Horváth, Tomasz Kania

We show that there is no real or complex indecomposable Banach space with the primary factorisation property (PFP). We relate the PFP of a Banach space $E$ to ring-theoretic infini…

math.FA2026

Preservation of primariness under $ℓ_{1}$ -, $c_{0}$ -, and $ℓ_{\infty}$ -sums of Banach spaces

Antonio Acuaviva

We prove transfer principles for the uniform primary factorisation property (UPFP) from a Banach space $X$ to the vector-valued sequence spaces $ℓ_{1} (X)$ , $c_{0} (X)$ and $\ell_\inf…

math.FA2026

Primariness of the spaces $ℓ_{p} (C (K))$ for $1 \leq p \leq \infty$

Antonio Acuaviva

We prove that the spaces $ℓ_{p} (C (α))$ and $ℓ_{p} (C [0, 1])$ have the uniform primary factorisation property whenever $α$ is an ordinal and $1 < p \leq \infty$ . For the case $p = 1$ , we…

math.FA2026

Primariness and the Primary Factorisation Property

Antonio Acuaviva, Tomasz Kania

We study the relation between primariness of Banach spaces and the stronger operator-theoretic notions of the primary factorisation property (PFP) and the uniform primary factorisa…

math.FA2025

$C (K)$ -spaces with few operators relative to posets

Antonio Acuaviva

Extending a method developed by Koszmider and Laustsen for constructing $C (K)$ -spaces we produce families of $C (K)$ -spaces with few operators relative to a partially ordered set $\…

math.FA2025

The class of Banach lattices is not primary

Antonio Acuaviva

Building on a recent construction of Plebanek and Salguero-Alarcón, which solved the Complemented Subspace Problem for $C (K)$ -spaces, and the subsequent work of De Hevia, Martínez-…

math.FA2025

Quantifying (non-)weak compactness of operators on $A L$ - and $C (K)$ -spaces

Antonio Acuaviva, Amir Bahman Nasseri

We study the representation of non-weakly compact operators between $A L$ -spaces. In this setting, we show that every operator admits a best approximant in the ideal of weakly compa…

math.FA2025★ 1 cited

Operators on injective tensor products of separable Banach spaces and spaces with few operators

Antonio Acuaviva

We give a characterization of the operators on the injective tensor product $E \otimes^_{ε} X$ for any separable Banach space $E$ and any (non-separable) Banach space…

math.FA2025

Complemented subspaces of a $C (K)$ -space constructed by Candido

Antonio Acuaviva

We classify the complemented subspaces of $C_{0} (L \times L)$ , where $L$ is an exotic locally compact Hausdorff space recently constructed by Candido under Ostaszewski's $♣$ -…

math.FA2024★ 1 cited

Factorizations and minimality of the Calkin Algebra norm for $C (K)$ -spaces

Antonio Acuaviva

For a scattered, locally compact Hausdorff space $K$ , we prove that the essential norm on the Calkin algebra \break $B (C_{0} (K)) / K (C_{0} (K))$ is a minimal algebra n…

A negative solution to the complemented subspace problem for Banach spaces with unconditional bases

Banach's Isometric Conjecture over the Complex Field

Mathematical Discovery in the Wild: AI-Guided Proofs in Banach Space Theory

A Unital Banach Algebra Which Is Not a Calkin Algebra

A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual

Pure infiniteness and primary factorisation

Preservation of primariness under ℓ1​-, c0​-, and ℓ∞​-sums of Banach spaces

Primariness of the spaces ℓp​(C(K)) for 1≤p≤∞

Primariness and the Primary Factorisation Property

C(K)-spaces with few operators relative to posets

The class of Banach lattices is not primary

Quantifying (non-)weak compactness of operators on AL- and C(K)-spaces

Operators on injective tensor products of separable Banach spaces and spaces with few operators

Complemented subspaces of a C(K)-space constructed by Candido

Factorizations and minimality of the Calkin Algebra norm for C(K)-spaces

Preservation of primariness under $ℓ_{1}$ -, $c_{0}$ -, and $ℓ_{\infty}$ -sums of Banach spaces

Primariness of the spaces $ℓ_{p} (C (K))$ for $1 \leq p \leq \infty$

$C (K)$ -spaces with few operators relative to posets

Quantifying (non-)weak compactness of operators on $A L$ - and $C (K)$ -spaces

Complemented subspaces of a $C (K)$ -space constructed by Candido

Factorizations and minimality of the Calkin Algebra norm for $C (K)$ -spaces