Everything about Weak trace-class operator
Mathematical concept
In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence. When the dimension of H is infinite, the ideal of weak trace-class operators is strictly larger than the ideal of trace class operators, and has fundamentally different properties. The usual operator trace on the trace-class operators does not extend to the weak trace class. Instead the ideal of weak trace-class operators admits an infinite number of linearly independent quasi-continuous traces, and it is the smallest two-sided ideal for which all traces on it are singular traces. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Weak trace-class operatorA 5-minute orientation
- Pick up a classic book: The Conspirators HierarchyThe most-reprinted book on the subject
- Go sideways: Singular traceA closely related topic
- Go sideways: Commutator subspaceA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
- No matching papers found.
📚 Books worth reading
The Conspirators HierarchyJohn Coleman · 1992
Perturbation theory for linear operatorsTosio Katō · 1966
Aspects of semidefinite programmingEtienne de Klerk · 2002- 📕The effect of foreign intervention on Somali conflict in Mogadishu, Somalia · 2014
The Human Planet · 2009
Mysteries in Bamboo VillageOpeyemi matthew adejobi · 2015
Prayer and actionErnest Edward Holmes · 1911
A TOUR OF THE WORLDMalik Mansab Khan, Muhammad Rafique Abdul Aziz · 2025
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Singular trace In mathematics, a singular trace is a trace on a space of linear operators of a separable Hilbert space that vanishes on operators of finite rank. Singular…
- Commutator subspace In mathematics, the commutator subspace of a two-sided ideal of bounded linear operators on a separable Hilbert space is the linear subspace spanned by…
- Calkin correspondence In mathematics, the Calkin correspondence, named after mathematician John Williams Calkin, is a bijective correspondence between two-sided ideals of bounded…
- Trace class In mathematics, specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is…
- Glossary of functional analysis This is a glossary for the terminology in a mathematical field of functional analysis. Throughout the article, unless stated otherwise, the base field…
- Spectral triple In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon…
- Banach space In mathematics, more specifically in functional analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space…
- Von Neumann algebra In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology…