Fredholm框架及其扰动

Fredholm frames and their perturbations

引入了Hilbert空间H的Fredholm框架概念,它是一种介于普通框架与Riesz基之间的一类特殊框架.应用算子论方法,给出了Fredholm框架的重要性质及其等价刻画,证明了H上全体Fredholm框架构成了由H中全体Bessel列组成的Banach空间中的开集.研究了Fredholm框架在小扰动下和算子扰动下的稳定性,证明了框架与Riesz基的膨胀不变性.

Fredholm frames for a Hilbert space H are introduced, which are special frames between frames and Riesz bases. By using operator theory method, some important properties and equivalent characterizations of Fredholm frames are obtained. It is proved that the set of all Fredholm frames for a Hilbert space H is an open set in the Banach space consisting of all Bessel sequences in H. It is proved that Fredholm frames are stable under small and operator perturbations. Inflations of frames and Riesz bases are also discussed.