论文标题
一些$ p $ beberling代数的对称性和逆闭合性
Symmetry and inverse-closedness of some $p$-Beurling algebras
论文作者
论文摘要
令$（g，d）$为度量空间，计数量度$μ$满足某些增长条件。令$ω（x，y）=（1+d（x，y））^δ$，对于$ 0 <δ\ leq1 $。令$ 0 <p \ leq1 $。令$ \ mathcal a_ {pΩ} $为$ g \ g \ times g $ on $ g \ times g $满足$ \ max \ {\ sup_x \ sum_y | k（x，y）|^pΩ（x，x，y）^p，\ sup_y \ sup_y \ sum_x | k（x，x，y）每个$ k \ in \ Mathcal a_ {pΩ} $在$ \ ell^2（g）$上定义了有限的线性操作员。此外，如果$ω$满足弱增长条件，那么我们表明$ \ Mathcal A_ {pΩ} $在$ b（\ ell^2（g））$中倒置。我们还将讨论超过$ \ Mathbb z^d $的无限矩阵的$ p $ -banach代数和$ p $ p $ -summable序列的$ \ mathbb z^{2d} $的$ p $ -banach代数。为了证明这些结果，我们证明了Hulanicki的引理和Barnes的引理$ P $ -BANACH代数。
Let $(G,d)$ be a metric space with the counting measure $μ$ satisfying some growth conditions. Let $ω(x,y)=(1+d(x,y))^δ$ for some $0<δ\leq1$. Let $0<p\leq1$. Let $\mathcal A_{pω}$ be the collection of kernels $K$ on $G\times G$ satisfying $\max\{\sup_x\sum_y |K(x,y)|^pω(x,y)^p, \sup_y\sum_x |K(x,y)|^pω(x,y)^p\}<\infty$. Each $K \in \mathcal A_{pω}$ defines a bounded linear operator on $\ell^2(G)$. If in addition, $ω$ satisfies the weak growth condition, then we show that $\mathcal A_{pω}$ is inverse closed in $B(\ell^2(G))$. We shall also discuss inverse-closedness of $p$-Banach algebra of infinite matrices over $\mathbb Z^d$ and the $p$-Banach algebra of weighted $p$-summable sequences over $\mathbb Z^{2d}$ with the twisted convolution. In order to show these results, we prove Hulanicki's lemma and Barnes' lemma for $p$-Banach algebras.
