[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 …
Conditions Implying Self-adjointness and Normality of Operators
H Stanković - Complex Analysis and Operator Theory, 2024 - Springer
In this paper, we give new characterizations of self-adjoint and normal operators on a Hilbert
space H. Among other results, we show that if H is a finite-dimensional Hilbert space and …
space H. Among other results, we show that if H is a finite-dimensional Hilbert space and …
On the invertibility of the sum of operators
MH Mortad - Analysis Mathematica, 2020 - Springer
The primary purpose of this paper is to investigate the question of the invertibility of the sum
of operators in the bounded and unbounded setting. Some interesting examples and …
of operators in the bounded and unbounded setting. Some interesting examples and …
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 …
[PDF][PDF] Unbounded generalizations of the Fuglede-Putnam theorem
arXiv:2203.06715v1 [math.FA] 13 Mar 2022 Page 1 arXiv:2203.06715v1 [math.FA] 13 Mar
2022 UNBOUNDED GENERALIZATIONS OF THE FUGLEDE-PUTNAM THEOREM SOUHEYB …
2022 UNBOUNDED GENERALIZATIONS OF THE FUGLEDE-PUTNAM THEOREM SOUHEYB …
[PDF][PDF] On the commutativity of unbounded unclosed symmetric operators
MS MOKTHAR-KHARROUBI… - Preprint posted on … - researchgate.net
ON THE COMMUTATIVITY OF UNBOUNDED UNCLOSED SYMMETRIC OPERATORS 1.
Introduction First, we assume readers are well acquainted with Page 1 ON THE …
Introduction First, we assume readers are well acquainted with Page 1 ON THE …
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 …