Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory

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.

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On nonselfadjoint operator algebras

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1990-0986648-8 ◽

1990 ◽

Vol 110 (4) ◽

pp. 915-915

Author(s):

Edward G. Effros ◽

Zhong-Jin Ruan

Keyword(s):

Operator Algebras ◽

Nonselfadjoint Operator

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

Applied Sciences ◽

10.3390/app11209542 ◽

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.

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