On the range of upper triangular relation matrices
Yanyan Du, Junjie Huang, Ran Huo · Linear and Multilinear Algebra · 2021
Let H and K be infinite-dimensional separable Hilbert spaces, and denote by MC:=AC0B the upper triangular linear relation matrix with unknown C in H⊕K. For given relations A and B, some necessary and sufficient conditions are presented under which the range of MC is (not) closed for any bounded operator and relation C:K→H based on certain appropriate space decompositions, respectively.