Abstract
The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Y. ArlinskiÏ and V. A. Zagrebnov, Around the van Daele-Schmüdgen Theorem, Integral Equations Operator Theory, 81 (2015), 53–95.
J. F. Brasche and H. Neidhardt, Has every symmetric operator a closed symmetric restriction whose square has a trivial domain?, Acta Sci. Math. (Szeged), 58 (1993), 425–430.
P. R. Chernoff A semibounded closed symmetric operator whose square has trivial domain, Proc. Amer. Math. Soc., 89 (1983), 289–290.
S. Dehimi and M. H. Mortad, Chernoff like counterexamples related to unbounded operators, Kyushu J. Math., to appear.
G. Jin and A. Chen, Some basic properties of block operator matrices, arXiv, (2014), arXiv: 1403.7732.
P. Jorgensen and F. Tian, Non-commutative analysis. With a foreword by Wayne Polyzou, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017.
H. Kosaki, On intersections of domains of unbounded positive operators, Kyushu J. Math., 60 (2006), 3–25.
M. Möller and F. H. Szafraniec, Adjoints and formal adjoints of matrices of unbounded operators, Proc. Amer. Math. Soc., 136 (2008), 2165–2176.
M. H. Mortad Counterexamples related to commutators of unbounded operators, Results Math., to appear.
M. Naimark, On the Square of a closed symmetric operator, Dokl. Akad. Nauk SSSR, 26 (1940), 866–870; ibid 28 (1940), 207–208.
S. Ôta and K. Schmüdgen, Some selfadjoint 2 x 2 operator matrices associated with closed operators, Integral Equations Operator Theory, 45 (2003), 475–484.
K. Schmüdgen, On domains of powers of closed symmetric operators, J. Operator Theory, 9 (1983), 53–75.
K. Schmüdgen, Unbounded Self-adjoint Operators on Hilbert Space, GTM 265, Springer, 2012.
Ch. Tretter, Spectral Theory of Block Operator Matrices and Applications, Imperial College Press, London, 2008.
J. Weidmann, Linear Operators in Hilbert Spaces, Springer, 1980.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by L. Molnár
Rights and permissions
About this article
Cite this article
Mortad, M.H. On the triviality of domains of powers and adjoints of closed operators. ActaSci.Math. 85, 651–658 (2019). https://doi.org/10.14232/actasm-018-857-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.14232/actasm-018-857-5