Absolutely (r,p,q)-summing inclusions

• Autorzy: Carsten Michels
• Języki publikacji: EN

Abstrakty

EN

As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 2. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of (u,s,t)-nuclear and of absolutely (r,p,q)-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary Banach sequence spaces and inclusions between finite-dimensional Schatten classes. Finally, applications to Hilbert numbers of inclusions are given.

Kategorie tematyczne

• 46M35: Abstract interpolation of topological vector spaces
• 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s -numbers, Kolmogorov numbers, entropy numbers, etc. of operators
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 1
• Strony: 19-45

Daty

wydano

2007

Twórcy

autor

Carsten Michels

• Department of Mathematics, University of Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany

Identyfikatory

DOI

10.4064/sm178-1-2