[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 …
Unbounded operators having self‐adjoint, subnormal, or hyponormal powers
We show that if a densely defined closable operator A is such that the resolvent set of A2 is
nonempty, then A is necessarily closed. This result is then extended to the case of a …
nonempty, then A is necessarily closed. This result is then extended to the case of a …
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 …
[PDF][PDF] On the triviality of domains of powers and adjoints of closed operators
MH Mortad - arXiv preprint arXiv:1811.09894, 2018 - arxiv.org
arXiv:1811.09894v1 [math.FA] 24 Nov 2018 Page 1 arXiv:1811.09894v1 [math.FA] 24 Nov 2018
ON THE TRIVIALITY OF DOMAINS OF POWERS AND ADJOINTS OF CLOSED OPERATORS …
ON THE TRIVIALITY OF DOMAINS OF POWERS AND ADJOINTS OF CLOSED OPERATORS …
On the operator equations An = A*A
Let n∈ N and let A be a closed linear operator (everywhere bounded or unbounded). In this
paper, we study (among others) equations of the type A∗ A= A n where n≥ 2 and see when …
paper, we study (among others) equations of the type A∗ A= A n where n≥ 2 and see when …
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] Counterexamples related to unbounded paranormal operators
MH Mortad - Examples and Counterexamples, 2021 - Elsevier
In this paper, we give an example of a densely defined non-closable paranormal operator.
Then, we give another example of a densely defined closable paranormal operator whose …
Then, we give another example of a densely defined closable paranormal operator whose …
Unbounded operators:(square) roots, nilpotence, closability and some related invertibility results
MH Mortad - arXiv preprint arXiv:2007.12027, 2020 - arxiv.org
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of
linear operators as well as some of their basic properties. The paper contains many …
linear operators as well as some of their basic properties. The paper contains many …
On the closedness of the range of (fractional) powers of certain classes of possibly unbounded operators
In this article, we establish certain identities about the closedness of the range of several
classes of possibly unbounded operators defined on a Hilbert space, such as self-adjoint …
classes of possibly unbounded operators defined on a Hilbert space, such as self-adjoint …
When nilpotence implies the zeroness of linear operators
arXiv:2008.09509v2 [math.FA] 29 Apr 2022 Page 1 arXiv:2008.09509v2 [math.FA] 29 Apr 2022
WHEN NILPOTENCE IMPLIES THE ZERONESS OF LINEAR OPERATORS NASSIMA FRID …
WHEN NILPOTENCE IMPLIES THE ZERONESS OF LINEAR OPERATORS NASSIMA FRID …