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Canonical static concept record

Trace-class operator

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Summary

A compact operator whose singular values are summable, permitting a basis-independent finite trace.

Record metadata

Canonical name: Trace-class operator
Concept ID: trace_class_operator
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Analysis
Domains: Analysis
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Operator ideal

Carrier(s)

Hilbert space $H$

Data

compact operator $T$

Axioms / constraints

sum of singular values is finite

Canonically induces

well-defined trace
ideal in bounded operators

Notes

Trace class is stronger than Hilbert–Schmidt class.

Concept sources

Wikipedia — Trace class — Trace class · encyclopedic reference · source ID wp-trace_class_operator
nLab — trace class — trace class · mathematical reference · source ID nlab-trace_class_operator
Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Bounded linear operator Trace-class operator

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: traceclass_from_operator
Relation type: Framework specialization framework-specialization
Direction: source → target
Endpoint roles: source: Specializes to; target: Special case or refinement of
Authored annotation: summable singular values

Authored explanation

Trace-class operators form an operator ideal with a finite trace norm.

How to interpret this relation type

A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.

Relation sources

Wikipedia — Bounded operator — Bounded operator · encyclopedic reference · source ID wp-bounded_linear_operator
nLab — bounded linear operator — bounded linear operator · mathematical reference · source ID nlab-bounded_linear_operator
Wikipedia — Trace class — Trace class · encyclopedic reference · source ID wp-trace_class_operator
nLab — trace class — trace class · mathematical reference · source ID nlab-trace_class_operator
Cambridge — Quantum Mechanics — Quantum Mechanics · University of Cambridge lecture notes · source ID tong-quantum

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.