Counterexamples undeniably play an outstanding role in mathematics. As is known,
counterexamples are patently examples but with a different purpose. The commonly agreed …

This book is for third and fourth year university mathematics students (and Master students)
as well as lecturers and tutors in mathematics and anyone who needs the basic facts on …

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 …

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 …

ON THE COMMUTATIVITY OF CLOSED SYMMETRIC OPERATORS Page 1 Analysis Math.,
49 (3) (2023), 721–731 DOI: 10.1007/s10476-023-0226-2 ON THE COMMUTATIVITY OF …

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 …

Let $ T\in B (H) $ be such that $ T^ n $ is self-adjoint for some $ n\in\mathbb {N} $ with $
n\geq 3$. The paper's primary aim is to establish the conditions that lead to the self …

Let and be elements of a complex unital Banach algebra. The numerical range
submultiplicity is investigated. As a consequence of the inclusions established, we confirm a …

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 …

A priori estimates for some differential operators Page 1 HAL Id: tel-03670712 https://hal.science/tel-03670712
Submitted on 9 Jun 2022 HAL is a multi-disciplinary open access archive for the deposit and …