An example of a sigma -compact infinite-dimensional pre-Hilbert space H is constructed such that any continuous linear operator T: H --> H is of the form T = lambdaI + F for some lambda is an element of R and for a finite-dimensional continuous linear operator F. A class of simple examples of pre-Hilbert spaces nonisomorphic to their closed hyperplanes is given. A sigma -compact pre-Hilbert space H isomorphic to H x R x R and nonisomorphic to H x R is also constructed.
|Number of pages||16|
|Journal||Russian Journal of Mathematical Physics|
|Publication status||Published - Jan 2001|
ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics