Compressions of Compact Tuples
MetadataShow full item record
We study the matrix range of a tuple of compact operators on a Hilbert space and examine the notions of minimal, nonsingular, and fully compressed tuples. In this pursuit, we refine previous results by characterizing nonsingular compact tuples in terms of matrix extreme points of the matrix range. Further, we find that a compact tuple A is fully compressed if and only if it is multiplicity-free and the Shilov ideal is trivial, which occurs if and only if A is minimal and nonsingular. Fully compressed compact tuples are therefore uniquely determined up to unitary equivalence by their matrix ranges. We also produce a proof of this fact which does not depend on the concept of nonsingularity.
Cite this version of the work
Benjamin Passer, Orr Shalit (2019). Compressions of Compact Tuples. UWSpace. http://hdl.handle.net/10012/14299
The following license files are associated with this item: