[图书][B] Counterexamples in operator theory
MH Mortad - 2022 - Springer
Counterexamples undeniably play an outstanding role in mathematics. As is known,
counterexamples are patently examples but with a different purpose. The commonly agreed …
counterexamples are patently examples but with a different purpose. The commonly agreed …
Certain properties involving the unbounded operators p (T), TT⁎, and T⁎ T; and some applications to powers and nth roots of unbounded operators
MH Mortad - Journal of Mathematical Analysis and Applications, 2023 - Elsevier
In this paper, we are concerned with conditions under which [p (T)]⁎= p‾(T⁎), where p (z) is
a one-variable complex polynomial, and T is an unbounded, densely defined, and linear …
a one-variable complex polynomial, and T is an unbounded, densely defined, and linear …
On normal products of selfadjoint operators
A necessary and sufficient condition for the product AB of a selfadjoint operator A and a
bounded selfadjoint operator B to be normal is given. Various properties of the factors of the …
bounded selfadjoint operator B to be normal is given. Various properties of the factors of the …
Conditions implying commutativity of unbounded self-adjoint operators and related topics
K Gustafson, MH Mortad - Journal of Operator Theory, 2016 - JSTOR
Let B be a bounded self-adjoint operator and let A be a nonnegative self-adjoint unbounded
operator. It is shown that if BA is normal, it must be self-adjoint and so must be AB …
operator. It is shown that if BA is normal, it must be self-adjoint and so must be AB …
Yet more versions of the Fuglede–Putnam theorem
MH Mortad - Glasgow Mathematical Journal, 2009 - cambridge.org
YET MORE VERSIONS OF THE FUGLEDE–PUTNAM THEOREM Page 1 Glasgow Math. J.
51 (2009) 473–480. C 2009 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089509005114 …
51 (2009) 473–480. C 2009 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089509005114 …
The Fuglede theorem and some intertwining relations
IFZ Bensaid, S Dehimi, B Fuglede… - Advances in Operator …, 2021 - Springer
In this paper, we show new versions of the Fuglede theorem in an unbounded setting. A
related counterexample is also presented. In the second part of the paper, we give a pair of …
related counterexample is also presented. In the second part of the paper, we give a pair of …
[HTML][HTML] Unbounded products of operators and connections to Dirac-type operators
K Gustafson, MH Mortad - Bulletin des Sciences Mathématiques, 2014 - Elsevier
Let A and B be two densely defined unbounded closeable operators in a Hilbert space such
that their unbounded operator products AB and BA are also densely defined. Then all four …
that their unbounded operator products AB and BA are also densely defined. Then all four …
Commutativity of unbounded normal and self-adjoint operators and applications
MH Mortad - arXiv preprint arXiv:1301.1632, 2013 - arxiv.org
arXiv:1301.1632v1 [math.FA] 8 Jan 2013 Page 1 arXiv:1301.1632v1 [math.FA] 8 Jan 2013
COMMUTATIVITY OF UNBOUNDED NORMAL AND SELF-ADJOINT OPERATORS AND …
COMMUTATIVITY OF UNBOUNDED NORMAL AND SELF-ADJOINT OPERATORS AND …
[HTML][HTML] Commutativity up to a factor for bounded and unbounded operators
C Chellali, MH Mortad - Journal of Mathematical Analysis and Applications, 2014 - Elsevier
In this paper, we further investigate the problem of commutativity up to a factor (or λ-
commutativity) in the setting of bounded and unbounded linear operators in a complex …
commutativity) in the setting of bounded and unbounded linear operators in a complex …