Proper improvements of well-known perturbation estimations for the parallel sum
F Kittaneh, A Zamani - Linear Algebra and its Applications, 2023 - Elsevier
Let A: B be the parallel sum of the positive semidefinite matrices A and B. In this paper, we
first establish an operator inequality involving A: B and then apply it to obtain some norm …
first establish an operator inequality involving A: B and then apply it to obtain some norm …
Generalized parallel sum of adjointable operators on Hilbert C*-modules
We introduce the notion of a tractable pair of operators as well as that of the generalized
parallel sum in the setting of adjointable operators on Hilbert C∗-modules. Some significant …
parallel sum in the setting of adjointable operators on Hilbert C∗-modules. Some significant …
[HTML][HTML] Operators on anti-dual pairs: Lebesgue decomposition of positive operators
Z Tarcsay - Journal of Mathematical Analysis and Applications, 2020 - Elsevier
In this paper we introduce and study absolute continuity and singularity of positive operators
acting on anti-dual pairs. We establish a general theorem that can be considered as a …
acting on anti-dual pairs. We establish a general theorem that can be considered as a …
The parallel sum in C*-algebras
Let A be a unital C∗-algebra with unit e and let a: b be the parallel sum of the two positive
definite elements a and b of A defined by a (a+ b)− 1 b. We show that the parallel sum a: b …
definite elements a and b of A defined by a (a+ b)− 1 b. We show that the parallel sum a: b …
[HTML][HTML] Shorting, parallel addition and form sums of nonnegative selfadjoint linear relations
YM Arlinskiĭ - Linear Algebra and its Applications, 2020 - Elsevier
We extend the operations of shorting and parallel addition from the cone of bounded
nonnegative selfadjoint operators in a Hilbert space to the set of all nonnegative selfadjoint …
nonnegative selfadjoint operators in a Hilbert space to the set of all nonnegative selfadjoint …
A generalized Schur complement for nonnegative operators on linear spaces
J Friedrich, M Günther, L Klotz - 2018 - projecteuclid.org
A generalized Schur complement for nonnegative operators on linear spaces Page 1 Banach
J. Math. Anal. 12 (2018), no. 3, 617–633 https://doi.org/10.1215/17358787-2017-0061 ISSN …
J. Math. Anal. 12 (2018), no. 3, 617–633 https://doi.org/10.1215/17358787-2017-0061 ISSN …
Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration
Á Göde, Z Tarcsay - arXiv preprint arXiv:2409.14068, 2024 - arxiv.org
The aim of this paper is to prove a general Lebesgue decomposition theorem for positive
operators on so-called anti-dual pairs, following the iterative approach introduced by …
operators on so-called anti-dual pairs, following the iterative approach introduced by …
Arlinskii's iteration and its applications
T Titkos - Proceedings of the Edinburgh Mathematical Society, 2019 - cambridge.org
Several Lebesgue-type decomposition theorems in analysis have a strong relation to the
operation called the parallel sum. The aim of this paper is to investigate this relation from a …
operation called the parallel sum. The aim of this paper is to investigate this relation from a …
Operators on anti-dual pairs
Z Tarcsay, Á Göde - Journal of Mathematical Analysis …, 2024 - unipub.lib.uni-corvinus.hu
Our purpose in this note is to investigate the order properties of positive operators from a
locally convex space into its conjugate dual. We introduce a natural generalization of the …
locally convex space into its conjugate dual. We introduce a natural generalization of the …
[HTML][HTML] Operators on anti-dual pairs: Supremum and infimum of positive operators
Z Tarcsay, Á Göde - Journal of Mathematical Analysis and Applications, 2024 - Elsevier
Our purpose in this note is to investigate the order properties of positive operators from a
locally convex space into its conjugate dual. We introduce a natural generalization of the …
locally convex space into its conjugate dual. We introduce a natural generalization of the …