Search results for " measurable function"
showing 2 items of 2 documents
On the admissibility of the space L_{0}(A, X) of vector-valued measurable functions
2013
We prove the admissibility of the space L_0(A,X) of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.
Lower Semi-frames, Frames, and Metric Operators
2020
AbstractThis 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.