Author:
Tarcsay Zsigmond,Sebestyén Zoltán
Abstract
AbstractWe provide necessary and sufficient conditions for a pair S, T of Hilbert space operators in order that they satisfy $$S^*=T$$
S
∗
=
T
and $$T^*=S$$
T
∗
=
S
. As a main result we establish an improvement of von Neumann’s classical theorem on the positive self-adjointness of $$S^*S$$
S
∗
S
for two variables. We also give some new characterizations of self-adjointness and skew-adjointness of operators, not requiring their symmetry or skew-symmetry, respectively.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference17 articles.
1. Arens, R.: Operational calculus of linear relations. Pac. J. Math. 11, 9–23 (1961)
2. Behrndt, J., Hassi, S., de Snoo, H.S.V.: Boundary Value Problems, Weyl Functions, and Differential Operators Monographs in Mathematics, vol. 108. Birkhäuser, Cham (2020)
3. Gesztesy, F., Schmüdgen, K.: On a theorem of Z. Sebestyén and Zs. Tarcsay. Acta Sci. Math. (Szeged) 85, 291–293 (2019)
4. Hassi, S., de Snoo, H.S.V., Szafraniec, F.H.: Componentwise and canonical decompositions of linear relations. Diss. Math. 465, 59 (2009)
5. Neumann, J.: Allgemeine Eigenwerttheorie hermitescher Funktionaloperatoren. Math. Ann. 102, 49–131 (1930)
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献