论文标题
耐寒的代数
The Hardy-Weyl algebra
论文作者
论文摘要
我们研究了由Hardy操作员$ H $生成的代数$ \ Mathcal {a} $和$ l^2 [0,1] $的$ x $的操作员$ m_x $乘以$ x $。我们称$ \ Mathcal {a} $是Hardy-Weyl代数。我们表明，紧凑型操作员的商与$λ$连续的代数和$λ$分析的函数代数是同构的。我们找到了由$ \ Mathcal {a} $生成的$ C^*$ - 代数的类似toeplitz的短序列。我们研究操作员$ z = h -m_x $，证明其点频谱为$（-1,0] \ cup \ mathbb {d}（1,1）$，并且特征值随着点的分数向左移至$ 0 $而增长。
We study the algebra $\mathcal{A}$ generated by the Hardy operator $H$ and the operator $M_x$ of multiplication by $x$ on $L^2[0,1]$. We call $\mathcal{A}$ the Hardy-Weyl algebra. We show that its quotient by the compact operators is isomorphic to the algebra of functions that are continuous on $Λ$ and analytic on the interior of $Λ$ for a planar set $Λ$ = $[-1,0] \cup \bar{ \mathbb{D}(1,1)}$, which we call the lollipop. We find a Toeplitz-like short exact sequence for the $C^*$-algebra generated by $\mathcal{A}$. We study the operator $Z = H - M_x$, show that its point spectrum is $(-1,0] \cup \mathbb{D}(1,1)$, and that the eigenvalues grow in multiplicity as the points move to $0$ from the left.
