Abstract
In recent years, the concepts of frame in [Formula: see text]-Hilbert space and [Formula: see text]-frames in [Formula: see text]-Hilbert space have been introduced. The [Formula: see text]-frames in the [Formula: see text]-Hilbert space are more generalized than the ordinary frames. This paper deals with the problem of sum of [Formula: see text]-frames in [Formula: see text]-Hilbert space. First, the sufficient condition for the finite sum of [Formula: see text]-frames and Bessel sequences in [Formula: see text]-Hilbert space is given. Then, some results on the operator [Formula: see text] and pre-frame operator are given, and some new results on the sum of [Formula: see text]-frame are proved. We then discuss several results for the perturbation and stability of the [Formula: see text]-frames in [Formula: see text]-Hilbert space about the sum of the [Formula: see text]-frames.
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