Definition talk:Zero Operator

We have already started using the terminology Definition:Annihilator for the same concept in ring theory -- is the same apprpriate here? --prime mover (talk) 10:03, 23 July 2017 (EDT)


 * Oops...sorry I did not notice that. Shall we extend the definition of annihilator to the Hilbert Spaces, then prove that zero operator is in $\operatorname{Ann}(H)$, or use annihilator to define zero operator instead? I am not sure about it. -- Z423x5c6 (talk) 11:54, 23 July 2017 (EDT)


 * Without knowing enough about it to be be authoritative ... my approach would be: set up a general parent page "Annihilator", with subpages for the various contexts. As a Hilbert space is (to the best of my knowledge) a vector space with an infinite number of dimensions, the same definition should be usable for both -- and if any proof of that fact is needed, we add a separate page to demonstrate it.


 * We may also want to link to the "zero element" of a ring, and even a "zero element" of a general algebraic structure as it is defined, and pull it all together as an instance of the same concept.


 * Obviously an "also known as" is to be considered, as an "annihilator" and "zero operator" seem to be the same thing. Whether we make the main page "zero operator" with "annihilator" identified as its "also known as" is a detail that is ultimately unimportant, but will depend on how much rework we would need to do to maintain consistency. --prime mover (talk) 14:43, 23 July 2017 (EDT)