Electronic Resource
Springer
Integral equations and operator theory
3 (1980), S. 463-469
ISSN:
1420-8989
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01701502
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