English Scientific Article (Journal Article)

- SJR Scopus - Algebra and Number Theory: Q2

Identifiers

- MTMT: 30446535
- DOI: 10.1080/03081087.2018.1430120
- EDIT: 40611
- WoS: 000457976200016
- Scopus: 85041217613

Subjects:

In general, it is a non-trivial task to determine the adjoint S* of an unbounded operator
S acting between two Hilbert spaces. We provide necessary and sufficient conditions
for a given operator T to be identical with S*. In our considerations, a central role
is played by the operator matrix M-S,M-T = (I -T S I). Our approach has several consequences
such as characterizations of closed, normal, skew- and selfadjoint, unitary and orthogonal
projection operators in real or complex Hilbert spaces. We also give a self-contained
proof of the fact that T*T always has a positive selfadjoint extension.

2021-05-09 12:41