arXiv subjects

Alonso Delfín

Publications and source records attributed to Alonso Delfín.

6 recordsLinked to original sources

arXiv2026

Twisted crossed products of Banach algebras

Given a locally compact group $G$, a nondegenerate Banach algebra $A$ with a contractive approximate identity, a twisted action $(α, σ)$ of $G$ on $A$, and a family $\mathcal{R}$ of uniformly bounded representations of $A$ on Banach spaces, we define the twisted crossed product $F_\mathcal{R}(G,A,α, σ)$. When $\mathcal{R}$ consists of contractive representations, we show that $F_\mathcal{R}(G,A,α, σ)$ is a Banach algebra with a contractive approximate identity, which can also be characterized by an isometric universal property. As an application, we specialize to the $L^p$-operator algebra setting, defining both the $L^p$-twisted crossed product and the reduced version. Finally, we give a generalization of the so-called Packer-Raeburn trick to the $L^p$-setting, showing that any $L^p$-twisted crossed product is "stably" isometrically isomorphic to an untwisted one.

math.FA↗

arXiv2026

C*-like modules and matrix $p$-operator norms

We present a generalization of Hölder duality to algebra-valued pairings via $L^p$-modules. Hölder duality states that if $p \in (1, \infty)$ and $p^{\prime}$ are conjugate exponents, then the dual space of $L^p(μ)$ is isometrically isomorphic to $L^{p^{\prime}}(μ)$. In this work we study certain pairs $(\mathsf{Y},\mathsf{X})$, as generalizations of the pair $(L^{p^{\prime}}(μ), L^p(μ))$, that have an $L^p$-operator algebra valued pairing $\mathsf{Y} \times \mathsf{X} \to A$. When the $A$-valued version of Hölder duality still holds, we say that $(\mathsf{Y},\mathsf{X})$ is C*-like. We show that finite and countable direct sums of the C*-like module $(A,A)$ are still C*-like when $A$ is any block diagonal subalgebra of $d \times d$ matrices. We provide counterexamples when $A \subset M_d^p(\mathbb{C})$ is not block diagonal.

math.FA↗

arXiv2025

$L^p$-spectral triples and $p$-quantum compact metric spaces

For $p \in [1, \infty)$, we generalize the concept of classical spectral triples by extending the framework from Hilbert spaces to $L^p$-spaces, and from C*-algebras to $L^p$-operator algebras. In addition, we define an $L^p$-spectral triple to be metric when the state space of the algebra has a $p$-quantum compact metric space structure. Specifically, we construct $L^p$-spectral triples for reduced $L^p$-group algebras of countable discrete groups with proper length functions and also for $L^p$ UHF-algebras of infinite tensor product type, the latter inspired by E. Christensen and C. Ivan's construction of a Dirac operator on AF C*-algebras. We prove that $L^p$-spectral triples associated with $L^p$-group algebras (provided that the length function is of bounded doubling) and those associated with $L^p$ UHF-algebras are always metric.

math.FA↗

arXiv2025

$L^p$-modules and $L^p$-correspondences

We introduce an $L^p$-operator algebraic analogue of Hilbert C*- modules. We present the theory of concrete $L^p$-modules, their morphisms, and basic constructions including countable direct sums and tensor products. We then define $L^p$-correspondences and the interior tensor product of these.

math.FA↗

arXiv2024

Multiplier algebras of $L^p$-operator algebras

It is known that the multiplier algebra of an approximately unital and nondegenerate $L^p$-operator algebra is again an $L^p$-operator algebra. In this paper we investigate examples that drop both hypotheses. In particular, we show that the multiplier algebra of $T_2^p$, the algebra of strictly upper triangular $2 \times 2$ matrices acting on $\ell_2^p$, is still an $L^p$-operator algebra for any $p$. To contrast this result, we first provide a thorough study of the augmentation ideal of $\ell^1(G)$ for a discrete group $G$. We use this ideal to define a family of nonapproximately unital degenerate $L^p$-operator algebras, $F_{0}^p(\Bbb{Z}/3\Bbb{Z})$, whose multiplier algebras cannot be represented on any $L^q$-space for any $q \in [1, \infty)$ as long as $p \in [1, p_0] \cup [p_0', \infty)$, where $p_0=1.606$ and $p_0'$ is its Hölder conjugate.

math.FA↗

arXiv2024

Representations of C*-correspondences on pairs of Hilbert spaces

We study representations of Hilbert bimodules on pairs of Hilbert spaces. If $A$ is a C*-algebra and $\mathsf{X}$ is a right Hilbert $A$-module, we use such representations to faithfully represent the C*-algebras $\mathcal{K}_A(\mathsf{X})$ and $\mathcal{L}_A(\mathsf{X})$. We then extend this theory to define representations of $(A,B)$ C*-correspondences on a pair of Hilbert spaces and show how these can be obtained from any nondegenerate representation of $B$. As an application of such representations, we give necessary and sufficient conditions on an $(A,B)$ C*-correspondences to admit a Hilbert $A$-$B$-bimodule structure. Finally, we show how to represent the interior tensor product of two C*-correspondences.

math.OA↗