The spectra of closed interpolated operators |
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Authors: | Yin Chen |
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Institution: | (1) Department of Mathematical Science, Lakehead University, P7B 1E1 Thunder Bay, Ontario, Canada |
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Abstract: | Let (E
0,E
1) be a compatible couple of Banach spaces, and letE
: 0Re1 be the complex interpolation spaces ofE
0,E
1. LetT be a closed linear operator onE
0+E
1, then the restrictionT
ofT to eachE
is closed. If we denote by
the extended spectrum ofT
inE
, then, under appropriate conditions, it is shown that the map
is an analytic multifunction in the strip {C0<Re<1}. We use these results to give some applications to the spectral theory of semigroups. |
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Keywords: | 46B70 47A10 |
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