Hilbert空间上框架的扰动

Perturbation of frame on a Hilbert space

研究了Hilbert空间上框架的扰动问题.应用算子论的方法,给出了当f={fi}i∈Z是框架时,序列{λifi}i∈Z,{Tfi}i∈Z及{Tifi}i∈Z成为框架的条件;证明了当f为框架,g为Bessel列且T 满足一定条件时,g也是一个框架.

The perturbation question on frame for a separable Hilbert space is discussed. By using operator theoretic method, some conditions for the sequences {λifi}i∈Z,{Tfi}i∈Z and {Tifi}i∈Z to be frames when {fi}i∈Z is a frame are given. It is also shown that if f is a frame, g is a Bessel sequence and T*f-g satisfies certain condition, then g is a frame.