Tsirelson like operator spaces

TL;DR

This paper constructs new examples of weak-$C_p$ operator spaces that closely resemble classical $C_p$ spaces, using methods inspired by Tsirelson's space, advancing understanding of non-homogeneous Hilbertian operator spaces.

Contribution

It introduces nontrivial weak-$C_p$ operator spaces with local structures similar to $C_p$, expanding the class of known operator space examples.

Findings

Constructed nontrivial weak-$C_p$ operator spaces

Examples are non-homogeneous Hilbertian operator spaces

Construction method parallels Tsirelson's space

Abstract

We construct nontrivial examples of weak-$C_p$ ($1\leq p \leq \infty$) operator spaces with the local operator space structure very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are non-homogeneous Hilbertian operator spaces, and their constructions are similar to that of 2-convexified Tsirelson's space by W. B. Johnson.