Alphabeta MathCompact Self Adjoint Hilbert Schmidt and Trace Class Operators — Examples
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2 · Logical flowchart
3 · Items
Example
Diagonal Schatten class criteria on ell two
Example
Volterra operator is Hilbert Schmidt and quasinilpotent
Example
Adjoint, norm and trace of an operator of rank at most one
Example
Integral operator trace under a valid diagonal hypothesis
Counterexample
Compact does not imply Hilbert Schmidt
Counterexample
Hilbert Schmidt does not imply trace class
Counterexample
The unilateral shift obstructs a cyclic linear trace extension
Remark
Schatten p classes
Sources
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §3.5–§3.6, diagonal operators and Schatten classes
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §3.1 and §3.6, the Volterra operator
- Anthony W. Knapp, Advanced Real Analysis — Chapter II, §5, rank-one operators
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §10.5, Lemma 10.26 and Theorem 10.27 (Mercer, printed pp. 304–306)
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §3.6, compact but not Hilbert–Schmidt diagonal operators
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §3.6, Hilbert–Schmidt but not trace-class diagonal operators
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §3.6, the shift and the failure of cyclicity without trace class
- Gerald Teschl, Topics in Real and Functional Analysis, version November 17, 2017 — §3.6, Schatten classes
- Anthony W. Knapp, Advanced Real Analysis — Chapter II, §5