Homework Help Overview
The discussion revolves around constructing an example of a linear operator on a Hilbert space that has an empty spectrum. The original poster notes the challenge of finding such an operator, especially since they can easily identify examples with an empty point spectrum but not an empty spectrum overall. They express uncertainty about how to begin this construction, particularly in the context of unbounded operators.
Discussion Character
- Exploratory, Assumption checking
Approaches and Questions Raised
- Participants question the definitions of "operator on Hilbert space" and "spectrum," emphasizing the importance of details such as the domain's density. There is a discussion about the nature of the operator's domain and whether it must encompass the entire Hilbert space.
Discussion Status
Some participants have provided clarifications regarding definitions and have referenced literature that may assist in understanding the problem better. There is an ongoing exploration of the requirements for the operator and the implications of its properties.
Contextual Notes
There is mention of constraints such as the lack of access to mathematical texts for some participants, which may limit their ability to reference established examples or definitions. The original poster seems to be under the impression that the task is to provide a means of constructing an operator rather than stating one explicitly.
