论文标题
Lipschitz p-bessel序列的乘数公制空间
Multipliers for Lipschitz p-Bessel sequences in metric spaces
论文作者
论文摘要
Schatten在1960年使用正交序列引入了希尔伯特空间中乘数的概念，并在2007年使用Bessel序列概括了Balazs。拉希米（Rahimi）和巴拉兹（Balazs）在2010年使用p-bessel序列将其扩展到Banach空间。在本文中，我们通过考虑Lipschitz功能进一步扩展了这一点。在途中，我们为公制空间定义了框架，该帧扩展了Banach空间的框架和Bessel序列的概念。我们表明，当符号序列收敛到零时，乘数是Lipschitz紧凑型操作员。我们研究乘数中参数的变化如何影响乘数的性质。
The notion of multipliers in Hilbert space was introduced by Schatten in 1960 using orthonormal sequences and was generalized by Balazs in 2007 using Bessel sequences. This was extended to Banach spaces by Rahimi and Balazs in 2010 using p-Bessel sequences. In this paper, we further extend this by considering Lipschitz functions. On the way we define frames for metric spaces which extends the notion of frames and Bessel sequences for Banach spaces. We show that when the symbol sequence converges to zero, the multiplier is a Lipschitz compact operator. We study how the variation of parameters in the multiplier effects the properties of multiplier.
