广义Riesz基的双正交特征刻画

Biorthogonal Characterization of Generalized Riesz Bases

本文利用广义双正交序列研究广义Riesz基的等价刻画,得到了算子序列是广义Riesz基当且仅当该算子列是广义完备的广义Bessel序列,且它存在广义双正交序列及这个双正交序列也是广义完备的广义Bessel序列.进一步证明了等价刻画中两个广义Bessel序列的广义完备性条件可以去掉一个(或者任一个),并举例说明了广义双正交,广义完备与广义Bessel条件之间的关系.

In this paper,we investigate the characterization of g-Riesz bases in term of g-biorthogonal sequences.We obtain that a sequence of operators is a g-Riesz basis if and only if it is a g-complete g-Bessel sequence with g-biorthogonal sequence which is also a g-complete g-Bessel sequence,and further prove that the condition for gcompleteness of one(any one) of two g-Bessel sequences can be removed from the characterization.Examples are given to illustrate the relations for g-biorthogonality,g-completeness and g-Bessel condition.