Unbounded operators having self‐adjoint, subnormal, or hyponormal powers

S Dehimi, MH Mortad - Mathematische Nachrichten, 2023 - Wiley Online Library
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 …

Certain properties involving the unbounded operators p (T), TT⁎, and T⁎ T; and some applications to powers and nth roots of unbounded operators

MH Mortad - Journal of Mathematical Analysis and Applications, 2023 - Elsevier
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 …

Extensions of positive symmetric operators and Krein's uniqueness criteria

Z Sebestyén, Z Tarcsay - Linear and Multilinear Algebra, 2024 - Taylor & Francis
We revise Krein's extension theory of positive symmetric operators. Our approach using
factorization through an auxiliary Hilbert space has several advantages: it can be applied to …

Operational calculus for rows, columns, and blocks of linear relations

S Hassi, JP Labrousse, H de Snoo - Advances in Operator Theory, 2020 - Springer
Columns and rows are operations for pairs of linear relations in Hilbert spaces, modelled on
the corresponding notions of the componentwise sum and the usual sum of such pairs. The …

On the adjoint of linear relations in Hilbert spaces

A Sandovici - Mediterranean Journal of Mathematics, 2020 - Springer
Assume that HH and KK are two real or complex Hilbert spaces, A a linear relation from HH
to KK, and B a linear relation from KK to HH, respectively. Necessary and sufficient …

Range-kernel characterizations of operators which are adjoint of each other

Z Tarcsay, Z Sebestyén - Advances in Operator Theory, 2020 - Springer
We provide necessary and sufficient conditions for a pair S, T of Hilbert space operators in
order that they satisfy S^*= TS∗= T and T^*= ST∗= S. As a main result we establish an …

The class of 𝒮-operators on Hilbert space

ES Abdulwahid - Journal of Interdisciplinary Mathematics, 2022 - Taylor & Francis
The aim of this research is to introduce a new type of operator on Hilbert space which is
called 𝒮-operator. The operator namely 𝒮-operator if, where adjoint operator of. Thus some …

Operators on anti‐dual pairs: Generalized Krein–von Neumann extension

Z Tarcsay, T Titkos - Mathematische Nachrichten, 2021 - Wiley Online Library
The main aim of this paper is to generalize the classical concept of a positive operator, and
to develop a general extension theory, which overcomes not only the lack of a Hilbert space …

On the spectral theory of linear differential-algebraic equations with periodic coefficients

B Alshammari, A Welters - Analysis and Mathematical Physics, 2023 - Springer
In this paper, we consider the spectral theory of linear differential-algebraic equations
(DAEs) for periodic DAEs in canonical form, ie, J df dt+ H f= λ W f, where J is a constant skew …

Some results concerning the linear relations which are adjoint to each other

A Ammar, N Lazrag - Rendiconti del Circolo Matematico di Palermo Series …, 2023 - Springer
In order to study the stability of self-adjointness of a block linear relation matrix with
unbounded entries acting in Hilbert spaces, we start by discussing the question whether a …