Traces and Shift Invariant Functionals

DOI10.1002/MANA.19901450102zbMath0709.47021OpenAlexW2014559781MaRDI QIDQ3492192

Albrecht Pietsch

Publication date: 1990

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.19901450102

zbMATH Keywords

approximation numbersBanach limit- constructionscontinuous trace on quasi-Banach operator idealsnon-standard shift-invariant functionalsrearrangement invariant functionalsSchatten-type iealsshift invariant functionals on certain sequence spaces

Mathematics Subject Classification ID

Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Operator ideals (47L20)

Related Items (20)

The existence of singular traces on simply generated operator ideals ⋮ Quasi-Banach operator ideals with a very strange trace ⋮ Banach limits and traces on \(\mathcal{L}_{1, \infty}\) ⋮ An upper triangular decomposition theorem for some unbounded operators affiliated to \(\mathrm{II}_{1}\)-factors ⋮ A new view at Dixmier traces on \(\mathfrak{L}_{1,\infty} (H)\) ⋮ Traces on operator ideals defined over the class of all Banach spaces and related open problems ⋮ A new approach to operator ideals on Hilbert space and their traces ⋮ Traces and symmetric linear forms ⋮ Which traces are spectral? ⋮ Geometry of Banach limits and their applications ⋮ Advances in Dixmier traces and applications ⋮ Traces of Hilbert space operators and their recent history ⋮ Connes integration formula for the noncommutative plane ⋮ Traces on operator ideals and related linear forms on sequence ideals. II ⋮ Traces on operator ideals and related linear forms on sequence ideals. I ⋮ Completeness of quasi-normed operator ideals generated by \(s\)-numbers ⋮ Traces on operator ideals and related linear forms on sequence ideals. III ⋮ Traces and residues of pseudo-differential operators on the torus ⋮ Weierstrass functions separate all traces ⋮ Dixmier traces of operators on Banach and Hilbert spaces

Cites Work

• The Set of all Generalized Limits of Bounded Sequences
• Unnamed Item

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