• 대한수학회지
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• 제33권1호
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• pp.205-216
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• 1996

In [13], Ptak and Vrbova proved that if T is a bounded normal operator T on a complex Hilbert space H, then the ranges of the spectral projections can be represented in the form $$ \varepsilon(F)H = \bigcap_{\lambda\notinF} (T - \lambda I) H for all closed subsets F of C, $$ where $\varepsilon$ denotes the spectral measure associated with T.

• 대한수학회지
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• 제50권5호
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• pp.933-944
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• 2013

Based on the four kinds of theoretical definitions of the continuous module homomorphism between random locally convex modules, we first show that among them there are only two essentially. Further, we prove that such two are identical if the family of $L^0$-seminorms for the former random locally convex module has the countable concatenation property, meantime we also provide a counterexample which shows that it is necessary to require the countable concatenation property.