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 …

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 …

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 …

In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with
some examples. We also present results pertaining to the Hyers–Ulam stability of the sum …

A necessary and sufficient condition for the product AB of a selfadjoint operator A and a
bounded selfadjoint operator B to be normal is given. Various properties of the factors of the …

In this paper, we improve the famous Reid inequality related to linear operators. Some
monotony results for positive operators are also established with a different approach from …

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 …

Abstract Let A, B ∈ B (H) A, B∈ B (H). In the present paper, we establish simple and
interesting facts on when we have| A|| B|=| B|| A|| A|| B|=| B|| A|,| AB|=| A|| B|| AB|=| A|| B|,| A ± …

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 …