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

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 …

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 …

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 …

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 …

arXiv:2008.09509v2 [math.FA] 29 Apr 2022 Page 1 arXiv:2008.09509v2 [math.FA] 29 Apr 2022
WHEN NILPOTENCE IMPLIES THE ZERONESS OF LINEAR OPERATORS NASSIMA FRID …

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 M be a von Neumann algebra of operators on a Hilbert space H and τ be a faithful
normal semifinite trace on M, S (M, τ) be the∗-algebra of all τ-measurable operators …

TABLE OF CONTENTS Page 1 Advances in Applied Mathematics, Vol.13, No.1, 1-484 应用
数学进展, 13 卷1 期 Published Online January 2024 in Hans (https://www.hanspub.org/journal/aam) …

ON THE COMMUTATIVITY OF UNBOUNDED UNCLOSED SYMMETRIC OPERATORS 1.
Introduction First, we assume readers are well acquainted with Page 1 ON THE …