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Longfa Sun

Publications and source records attributed to Longfa Sun.

6 recordsLinked to original sources
arXiv2026

Hereditary Approximation under Hilbertian Extension

In this paper, we prove that if a Banach space $X$ has the hereditary approximation property, then $X\oplus_2 H$ has the hereditary approximation property for every Hilbert space $H$. This answers a question of Johnson and Szankowski. In addition, if $X$ is also reflexive, then every closed subspace of $X\oplus_2H$ has the metric approximation property. The proof uses Grothendieck's characterization of the approximation property, a factorization of nuclear operators through quotients of $X$, and a nuclear perturbation of the coordinate projection on a closed graph.

math.FA↗
arXiv2026

Very tight embeddings of subspaces of \(L_p\) for \(0<p<1\)

For \(0 1\), every \(d\)-dimensional subspace of \(L_p\) embeds linearly into \(\ell_p^{\lfloorμd\rfloor}\) with distortion at most \(C(p,μ)(\log(d+2))^{1/p}\). If its Rademacher type \(q\) constant is at most \(T\), where \(p<q\leq2\), the distortion is at most \(C(p,q,μ)T\), independently of \(d\). We also give explicit bounds as \(μ\downarrow1\). This answers the question of Johnson and Schechtman concerning the extension of their very tight embedding theorem below exponent one. The proof combines compression at a lower exponent with a change of density that preserves the number of coordinates, and applies over both scalar fields.

math.FA↗
arXiv2026

Hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups

We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant. The main ingredient of our proof is Meixner polynomials. The goal of this paper is twofold: to provide more examples of hypercontractive quantum Markov semigourps on non-tracial von Neumann algebras, and to determine the optimal order of the optimal time for quantum Ornstein-Uhlenbeck semigroups.

math.FA↗
arXiv2026

$\varepsilon$-isometries without isometric embeddings

We show that there exist two separable real Banach spaces $X$ and $Y$ such that, for every $\varepsilon>0$, there is a standard exact $\varepsilon$-isometry $f_\varepsilon: X\to Y$ whose distortion of every distance is between $0$ and $\varepsilon$, whereas no isometric embedding of $X$ into $Y$ exists, even without a linearity assumption. This gives a negative answer to \cite[Problem 1 and Problem 2]{cheng4} of Cheng and Zhou. The construction combines a snowflaked Lipschitz-free space with the Schur-property theorem of Kalton and the isometric linearization theorem of Godefroy and Kalton.

math.FA↗
arXiv2026

The Optimal Scaling Parameter in Metric Cotype for Alexandrov Spaces of Nonnegative Curvature

We determine the optimal order of the scaling parameter in the metric cotype $2$ inequality for complete Alexandrov spaces of nonnegative curvature. It grows linearly with the dimension $n$ of the discrete torus. This answers Question 17 of Eskenazis, Mendel, and Naor. In their sign-vector normalization on $\bigl(\mathbb{Z}/(2m\mathbb{Z})\bigr)^n$, the square of the optimal metric cotype $2$ constant for this class lies between $\max\{1,n/m\}$ and $e\lceil n/m\rceil$ for every dyadic $m\geq 2$. The upper bound follows from a dyadic Bernoulli-thinning argument using only the Lang--Schroeder--Sturm inequality. Snowflake universality of the fixed Wasserstein space $\mathcal{P}_2(\mathbb{R}^3)$ gives the $n/m$ lower bound.

math.FA↗
arXiv2020

On the sum of simultaneously proximinal sets

In this paper, we show that the sum of a compact convex subset and a simultaneously $τ$-strongly proximinal convex subset (resp. simultaneously approximatively $τ$-compact convex subset) of a Banach space X is simultaneously tau-strongly proximinal (resp. simultaneously approximatively $τ$-compact ), and the sum of weakly compact convex subset and a simultaneously approximatively weakly compact convex subset of X is still simultaneously approximatively weakly compact, where $τ$ is the norm or the weak topology. Moreover, some related results on the sum of simultaneously proximinal subspaces are presented.

math.FA↗