We study uniform approximation for operator learning on compact subsets of Banach spaces. We bound the recovery dimensions and the number of network parameters in terms of compact-set complexity, the target gauge, and recovery stability. For bounded linear operators with a separable domain, we characterize gauge approx...
For $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ and every separable Banach space $V$, we use an oracle-relative two-sorted finite-extension construction, whose oracle records the local rational structure of $V$, to construct a separable Banach space $X_V$ such that $$ \operatorname{Cal}(X_V)=\mathcal{B}(X_V)/\mathcal{K}(X_...
For a unital Banach algebra $A$ with $\|1_A\|=1$ and a decreasing sequence $(I_r)$ of proper closed two-sided ideals of finite codimension, we introduce the bounded detection envelope $$\widehat A:=\operatorname{Env}^{b}_{(I_r)}(A)=\varprojlim^{b}(A/I_r,\pi_r^s),\qquad \|(a_r)_r\|=\sup_r\|a_r\|.$$ Combining vector-valu...
The shuttle vehicle is a critical piece of handling equipment in automated logistics warehouses. As its primary load-bearing component, the load plate is subject to spatial constraints, requiring both a compact structure and effective prevention of structural deformation that could compress the battery. For a shuttle...
Rui-Ke Liu, Jie Shen, Meng Chen· SAE technical paper series· 0 citations
We prove a sufficient criterion for closed subspaces of operator spaces containing the finite-rank operators to have the uniform ball-covering property. Let $F$ be a separable uniformly convex Banach space, and let $\Lambda_F>1$ be a constant determined by its modulus of convexity. If $F$ has the $\pi_\lambda$-property...
Rui-Ke Liu, Jie Shen· 0 citations
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