Banach空间中p阶Bessel列的扰动

应用算子论方法研究Banach空间X中p(1i}_i∈I, 定义了有界线性算子Tf: X^*→l^p, 建立了从全体p阶Bessel列组成的Banach空间B^p_X(I)到算子空间B(X^*,l^p)上的等距线性同构α: f→T_f, 并给出了p阶Bessel列的扰动定理.

Perturbations of Bessel Sequences of Order p in a Banach Space

With the aid of operator theory, some perturbations of Bessel sequences of order p in a Banach space X were discussed. For a Bessel sequence f={f_i}_i∈I of order p in X, we defined a bounded linearoperator T_ffrom X^* into l^p and established a linear isometry isomorphism α from the space B^p_X(I) of all the Bessel sequences of order
p in a Banach space X into the operator space B(X^*,l^p) defined by α(f)=T_f. In the light of operator theory, some results on perturbations ofBessel sequences of order p were given, which are helpful to the study of frames of order p for a Banach space.