Digitale Medien
Springer
Integral equations and operator theory
3 (1980), S. 463-469
ISSN:
1420-8989
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract By the M.Riesz Convexity Theorem, an operator T on the space of simple integrable functions into the measurable functions (on some measure space) which has continuous extensions to Lp(μ) and Lq(μ) , where 1 ⩽ p ⩽ q ⩽ ∞ , also has continuous exten — sions to all Lr (μ) , p ⩽ r ⩽ q . It is shown that, whenever σ(Tp) and σ(Tq) are o-dimensional (in particular, countable) then the spectra σ(Tr) (p ⩽ r ⩽ q) are pairwise identical. For q = ∞ , only w*-continuous extensions are considered. An example due to Dayanithy shows that the conclusion fails in general.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01701502
Permalink
|
Standort |
Signatur |
Erwartet |
Verfügbarkeit |