On existence and construction of orthoscalar collections of subspaces

Abstract

This paper is devoted to the studu of orthoscalar tuples of subspaces in a complex Hilbert space, i.e. such that their orthoprojections sums up to a scalar operator. Such objects also known as tight fusion frames. They have a particularly usefulness in signal processing [3, 7, 8] and were studied in a number of works. For example, in [1] the question about possible values of the corresponding scalar was resolved. In [2] authors gave a criterion for existence of equal-rank tight fusion frames and presented a method for their construction, the so-called ’Spectral Tetris’. In this paper we present an explicit and simpler version of that criterion and supply it with a different proof.