Recent Advances in Operator Theory and Operator Algebras

2017 ◽  
Author(s):  
Hari Bercovici ◽  
David Kerr ◽  
Elias Katsoulis ◽  
Dan Timotin
Keyword(s):  
Operator Theory ◽  
Operator Algebras ◽  
Recent Advances

scholarly journals Abstract reflexive sublattices and completely distributive collapsibility

1998 ◽  
Vol 58 (2) ◽  
pp. 245-260 ◽  
Author(s):  
W. E. Longstaff ◽  
J. B. Nation ◽  
Oreste Panaia
Keyword(s):  
Banach Space ◽  
Operator Theory ◽  
Operator Algebras ◽  
Galois Connection ◽  
General Situation ◽  
Subspace Lattice ◽  
Complete Lattices ◽  
Completely Distributive ◽  
Subspace Lattices

There is a natural Galois connection between subspace lattices and operator algebras on a Banach space which arises from the notion of invariance. If a subspace lattice ℒ is completely distributive, then ℒ is reflexive. In this paper we study the more general situation of complete lattices for which the least complete congruence δ on ℒ such that ℒ/δ is completely distributive is well-behaved. Our results are purely lattice theoretic, but the motivation comes from operator theory.

scholarly journals Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC

2021 ◽  
Vol 11 (20) ◽  
pp. 9542
Author(s):  
David W. Kribs ◽  
Comfort Mintah ◽  
Michael Nathanson ◽  
Rajesh Pereira
Keyword(s):  
Operator Theory ◽  
Operator Algebras ◽  
Quantum States ◽  
Classical Communication ◽  
Quantum Operations ◽  
Graph Theoretic ◽  
Local Quantum ◽  
First Time ◽  
Theoretic Description ◽  
Theory Operator

We bring together in one place some of the main results and applications from our recent work on quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investigate the topic of distinguishability of sets of quantum states in quantum communication, with particular reference to the framework of one-way local quantum operations and classical communication (LOCC). We also derive a new graph-theoretic description of distinguishability in the case of a single-qubit sender.

scholarly journals Normed Dual Algebras

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 174 ◽  
Author(s):  
Sergey Ludkowski
Keyword(s):  
Operator Theory ◽  
Operator Algebras ◽  
Regular Algebras

This article is devoted to the investigation of dual and annihilator normed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and by using them, core radicals and radicals are investigated. Moreover, for this purpose ∗-algebras and finely regular algebras are also studied. Relations with operator theory and realizations of these algebras by operator algebras are outlined.

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