论文标题
序列空间上的广义伏尔泰拉运算符的准能力
Quasi-nilpotency of generalized Volterra operators on sequence spaces
论文作者
论文摘要
我们在权力系列的空间中研究了具有加权$ \ ell^p $ spaces $ 1 <p <+\ \ iftty $的泰勒系数。我们的主要结果是，当一个分析符号$ g $是加权$ \ ell^p $空间的倍增时，那么相应的广义Volterra运算符$ t_g $在同一空间和quasi-nilpotent上有限，即它的频谱是$ \ {0 \}。还结合了有关$ \ ell^p $空间的乘数的已知结果，我们给出了$ \ ell^p $上有界准广义的Quast-nilpotent Permorized Volterra运算符的非微不足道示例。 我们通过介绍我们称为下三角矩阵的Schur乘数的内容来解决问题，并在$ \ ell^p，1 <p <\ iftty $上构建了Schur乘数家族，用于下三角矩阵，与可总结内核有关。为了证明我们的结果的力量，我们还在$ \ ell^2 $上找到了Hankel运营商的新类Schur乘数，这扩展了E. Ricard的结果。
We study the quasi-nilpotency of generalized Volterra operators on spaces of power series with Taylor coefficients in weighted $\ell^p$ spaces $1<p<+\infty$ . Our main result is that when an analytic symbol $g$ is a multiplier for a weighted $\ell^p$ space, then the corresponding generalized Volterra operator $T_g$ is bounded on the same space and quasi-nilpotent, i.e. its spectrum is $\{0\}.$ This improves a previous result of A. Limani and B. Malman in the case of sequence spaces. Also combined with known results about multipliers of $\ell^p$ spaces we give non trivial examples of bounded quasi-nilpotent generalized Volterra operators on $\ell^p$. We approach the problem by introducing what we call Schur multipliers for lower triangular matrices and we construct a family of Schur multipliers for lower triangular matrices on $\ell^p, 1<p<\infty$ related to summability kernels. To demonstrate the power of our results we also find a new class of Schur multipliers for Hankel operators on $\ell^2 $, extending a result of E. Ricard.
