Abstract:

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 of Bessel sequences of order p were given, which are helpful to the study of frames of order p for a Banach space.

Key words: perturbation, Bessel sequence of order p, Banach space