Abstract of a paper by Venta Terauds
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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0804.3451 or http://arXiv.org/abs/0804.3451 or by email in unzipped form by transmitting an empty message with subject line uget 0804.3451 or in gzipped form by using subject line get 0804.3451 to: math@arXiv.org.
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alspach@fourier.math.okstate.edu