On the adjoint of Hilbert space operators

Sebestyen, Zoltan [Sebestyén, Zoltán (Funkcionálanalízis), author] Department of Applied Analysis and Computationa... (ELTE / ELU FoS / IM); Tarcsay, Zsigmond [Tarcsay, Zsigmond (Funkcionálanalízis), author] Department of Applied Analysis and Computationa... (ELTE / ELU FoS / IM)

English Scientific Article (Journal Article)
Published: LINEAR AND MULTILINEAR ALGEBRA 0308-1087 1563-5139 67 (3) pp. 625-645 2019
  • SJR Scopus - Algebra and Number Theory: Q2
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    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.
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    2021-05-09 12:41