This is an announcement for the paper "Functional calculus extensions on dual spaces" by Venta Terauds.
Abstract: In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one.
Archive classification: math.FA
Mathematics Subject Classification: 47B40
Remarks: 7 pages
The source file(s), func_calc_extns_terauds.tex: 24129 bytes, is(are) stored in gzipped form as 0804.3451.gz with size 7kb. The corresponding postcript file has gzipped size 70kb.
Submitted from: venta.terauds@newcastle.edu.au
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