Abstract
We present maximality results in the setting of non necessarily bounded operators. In particular, we discuss and establish results showing when the “inclusion” between operators becomes a full equality.
Similar content being viewed by others
References
Conway, J.B.: A Course in Functional Analysis, 2nd edn. Springer, Berlin (1990)
Devinatz, A., Nussbaum, A.E., von Neumann, J.: On the permutability of self-adjoint operators. Ann. Math. 62, 199–203 (1955)
Devinatz, A., Nussbaum, A.E.: On the permutability of normal operators. Ann. Math. 65, 144–152 (1957)
Gustafson, K., Mortad, M.H.: Unbounded products of operators and connections to dirac-type operators. Bull. Sci. Math. 138(5), 626–642 (2014)
Gustafson, K., Mortad, M.H.: Conditions implying commutativity of unbounded self-adjoint operators and related topics. J. Oper. Theory 76(1), 159–169 (2016)
Jung, Il Bong, Mortad, M.H., Stochel, J.: On normal products of selfadjoint operators. Kyungpook Math. J. 57, 457–471 (2017)
Mortad, M.H.: An all-unbounded-operator version of the Fuglede–Putnam theorem. Complex Anal. Oper. Theory 6(6), 1269–1273 (2012)
Mortad, M.H.: Commutativity of unbounded normal and self-adjoint operators and applications. Oper. Matrices 8(2), 563–571 (2014)
Mortad, M.H.: A criterion for the normality of unbounded operators and applications to self-adjointness. Rend. Circ. Mat. Palermo 64(1), 149–156 (2015)
Nussbaum, A.E.: A commutativity theorem for unbounded operators in Hilbert space. Trans. Am. Math. Soc. 140, 485–491 (1969)
Paliogiannis, F.C.: A generalization of the Fuglede-Putnam theorem to unbounded operators. J. Oper. 2015, 804353 (2015). https://doi.org/10.1155/2015/804353
Rudin, W.: Functional Analysis. International Series in Pure and Applied Mathematics, 2nd edn. McGraw-Hill Inc, New York (1991)
Schmüdgen, K.: Unbounded Self-Adjoint Operators on Hilbert Space, vol. 265. Springer GTM, New York (2012)
Sebestyén, Z., Stochel, J.: On suboperators with codimension one domains. J. Math. Anal. Appl. 360(2), 391–397 (2009)
Stochel, J.: An asymmetric Putnam–Fuglede theorem for unbounded operators. Proc. Am. Math. Soc. 129(8), 2261–2271 (2001)
Stochel, J., Szafraniec, F.H.: Domination of unbounded operators and commutativity. J. Math. Soc. Jpn. 55(2), 405–437 (2003)
Weidmann, J.: Linear Operators in Hilbert Spaces (translated from the German by J. Szücs), vol. 68, Springer, GTM, New York (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Meziane, M., Mortad, M.H. Maximality of linear operators. Rend. Circ. Mat. Palermo, II. Ser 68, 441–451 (2019). https://doi.org/10.1007/s12215-018-0370-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-018-0370-x