Some Properties of Elements from M(A) in the Context of 3D Signal Processing

Signal processing methods cannot be circumscribed to existing models but require some extensions of mathematical theories (operator theory, functional analysis) to enable the widening of more general spaces or the modelling using more general functions but with fewer properties satisfying theorems used in similar frameworks. In this context, one can expand the Hilbert space L-2 to a locally convex space, sequentially complete, extension required in terms of types of data that must be processed. Hence, there is a need to obtain some equivalent theorems which can characterize operators endowed with a certain type of limitation. In this paper, a study on such equivalent conditions for T (where T is a multiplier on a locally convex algebra A which has a closed range) is performed.