Matricial Coupling and Equivalence After Extension
Harm Bart, Vladislavi Eduardovic Tsekanovskii · Birkhäuser Basel eBooks · 1992
The purpose of this paper is to clarify the notions of matricial coupling and equivalence after extension. Matricial coupling and equivalence after extension are relationships that may or may not exist between bounded linear operators. It is known that matricial coupling implies equivalence after extension. The starting point here is the observation that the converse is also true: Matricial coupling and equivalence after extension amount to the same . For special cases (such as, for instance, Fredholm operators) necessary and sufficient conditions for matricial coupling are given in terms of null spaces and ranges. For matrices, the issue of matricial coupling is considered as a completion problem.