Citation Context

...and S. Gudder [2] studied, in the more general setting of von Neumann algebras, what they call almost sharp effects, and which are, precisely, operators like PQP , for P, Q ∈ P . These effects play a role in some problems of quantum mechanics. They found a characterization of the set Y, which is very useful in our approach. It should be mentioned that in a complete different setting, S. Nelson and M. Neumann [20] found, for matrices, a characterization of the spectrum of elements of X. It turns out that their conditions can be easily translated to the Arias-Gudder’s theorem. T. Oikhberg [21], [22] proved many results on operators which can be factorized as finite products of orthogonal projections. We close these comments by mentioning that some modern approaches to Heisenberg uncertainty principle, like those of Donoho and Stark [10] and Havin and Joricke [15] (see also the survey by Folland and Sitaram [11]) are based on the compactness and spectral properties of certain products PQ, where P and Q respectively project onto time-limited and band-limited signals. We describe the contents of the sections. Section 2 contains some preliminary results. In section 3 we study some propertie...

Citation Context

... M. Neumann [27] found, for matrices, a characterization of the spectrum of elements of X. It turns out that their conditions can be easily translated to the Arias-Gudder’s theorem. T. Oikhberg [28], =-=[29]-=- proved many results on operators which can be factorized as finite products of orthogonal projections. We close these comments by mentioning that some modern approaches to Heisenberg uncertainty prin...

Citation Context

...s two new equivalent statements for the commutativity of two orthogonal projectors. There are many results in the literature on products of orthogonal projectors and related topics; see, for example, =-=[1, 13]-=-. The two identities (23) and (24) are two fundamental results for the product of two orthogonal projectors. They can be used for dealing with various matrix expressions that involve products of two o...