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

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 …

CHERNOFF-LIKE COUNTEREXAMPLES RELATED TO UNBOUNDED OPERATORS Page 1
Kyushu J. Math. 74 (2020), 105–108 doi:10.2206/kyushujm.74.105 CHERNOFF-LIKE …

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 …

The book is intended as a text for a one-semester graduate course in operator theory to be
taught" from scratch'', not as a sequel to a functional analysis course, with the basics of the …

Let n∈ N and let A be a closed linear operator (everywhere bounded or unbounded). In this
paper, we study (among others) equations of the type A∗ A= A n where n≥ 2 and see when …

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 …

The primary purpose of this paper is to show the existence of normal square and nth roots of
some classes of bounded operators on Hilbert spaces. Two interesting simple results hold …

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 …