Interpolation of spectra |
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Authors: | H H Schaefer |
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Institution: | (1) Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 74 Tübingen, Germany |
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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() and Lq() , where 1 p q , also has continuous exten — sions to all Lr () , p r q . It is shown that, whenever (Tp) and (Tq) are o-dimensional (in particular, countable) then the spectra (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. |
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