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<p>In this study, we aim to provide results on generalized frames, i.e., <i>g</i>-frames and <i>K</i>-<i>g</i>-frames in Hilbert spaces. We first prove results on <i>g</i>-frames. As a result, we show that every g-Bessel sequence for a Hilbert space <i>H</i> can be extended to a tight <i>g</i>-frame for <i>H</i>. Also, we provide sufficient conditions under which the sum of two <i>g</i>-frames is a <i>g</i>-frame. Next, some results on <i>K</i>-<i>g</i>-frames are derived. Since similar to <i>g</i>-frames, in general, the sum of two <i>K</i>-<i>g</i>-frames for a Hilbert space <i>H</i> is not a <i>K</i>-<i>g</i>-frame, sufficient conditions under which the sum of two <i>K</i>-<i>g</i>-frames to be a <i>K</i>-<i>g</i>-frame are obtained.</p>

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Some properties of generalized frames in Hilbert spaces

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Javad Baradaran,
  • Asghar Rahimi

摘要

In this study, we aim to provide results on generalized frames, i.e., g-frames and K-g-frames in Hilbert spaces. We first prove results on g-frames. As a result, we show that every g-Bessel sequence for a Hilbert space H can be extended to a tight g-frame for H. Also, we provide sufficient conditions under which the sum of two g-frames is a g-frame. Next, some results on K-g-frames are derived. Since similar to g-frames, in general, the sum of two K-g-frames for a Hilbert space H is not a K-g-frame, sufficient conditions under which the sum of two K-g-frames to be a K-g-frame are obtained.