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| Commuting n-Tuples of Closed Operators which Possess Spectral Capacity |
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Citation： |
Hu Shanwen.Commuting n-Tuples of Closed Operators which Possess Spectral Capacity[J].Chinese Annals of Mathematics B,1987,8(2):156~169 |
| Page view： 878
Net amount： 722 |
Authors： |
Hu Shanwen; |
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| Abstract： |
This paper introduces the notions of commuting n-tuples of closed operetors which possess SVEP, SDP and spectral capacity respectively. A formula of analytic functional calculus for several commuting unbounded operators is found. With the help of the formula, it is proved that T has spectral capacity implies T has SDP and T has SDP implies T has SVEP. It is also proved that if T possesses spectral capacity \varepsilon and f_\xi is analytic on a neighbourhood of \sigma(T) for j=l, 2,\cdots, k, thenf(T) = (f_1(T),\cdots,f_k(T)) is decomposable, and the spectral capacity \varepsilon ^* of f(T) is uniquely determind by \varepsilon ^*(F) =\varepsilon(f^-1(F)\bigcap \sigma(T)). |
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