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 …

When I took a course on spectral theory some 25 years ago, the Fuglede theorem was not
part of the syllabus of that course. Indeed, that course was mainly directed toward …

We give a spectral analysis of some unbounded normal product HK of two self-adjoint
operators H and K (which appeared in [7]) and we say why it is not self-adjoint even if the …

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 classes of (n,m)-power D-normal and (n,m)-power D-quasi-normal operators Page 1
Operators and Matrices Volume 13, Number 3 (2019), 705–732 doi:10.7153/oam-2019-13-51 …

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 …

Abstract Let A= U| A| and B= V| B| be the polar decompositions of A ∈ B (H _1) and B ∈ B
(H _2) and let Com (A, B) stand for the set of operators X ∈ B (H _2, H _1) such that AX= XB …

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 …

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 …