[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 …
On the absolute value of unbounded operators
The primary purpose of the present paper is to investigate when relations of the types| AB|=|
A|| B|,| A±B|≤| A|+| B|,|| A|—| B||≤| A±B| and| Re A|≤| A|(among others) hold in an …
A|| B|,| A±B|≤| A|+| B|,|| A|—| B||≤| A±B| and| Re A|≤| A|(among others) hold in an …
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 …
Generalizations of Weiss' version of the Fuglede–Putnam theorem for unbounded operators
MH Mortad - Expositiones Mathematicae, 2024 - Elsevier
The present paper discusses Weiss' version of the Fuglede–Putnam theorem. We establish
three generalizations of this version, each of which involves unbounded normal operators …
three generalizations of this version, each of which involves unbounded normal operators …
On generalized powers of operators
On generalized powers of operators | Rendiconti del Circolo Matematico di Palermo Series
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Unbounded generalizations of the Fuglede-Putnam theorem and applications to the commutativity of self-adjoint operators
In this article, we prove and disprove several generalizations of unbounded versions of the
Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the …
Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the …
Some Applications
MH Mortad - The Fuglede-Putnam Theory, 2022 - Springer
In the beginning, why “some” applications only? The answer is pretty simple. The Fuglede
theorem's applications are abundant and cannot all be included in this survey. Recall that …
theorem's applications are abundant and cannot all be included in this survey. Recall that …