This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated with the function be dense. The study is done also with the help of the generalized frame operator associated with a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed, if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.

本文探讨了通过度量算子（即严格为正的自伴算子）将希尔伯特空间中的一个弱可度量函数转换为连续帧的可能性。一个必要条件是与该函数关联的分析运算符的域要密集。这项研究也是在与弱可测函数相关的广义框架算子的帮助下完成的，该函数具有比常规框架算子更好的性能。特别注意较低的半帧：实际上，如果分析算符的域很密集，则可以使用（特殊）度量算符将较低的半帧转换为Parseval帧。