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We consider conditions under which a continuous functional calculus for a Banach space operator T ?? L(X) may be extended to a bounded Borel functional calculus, and under which a functional calculus for absolutely continuous (AC) functions may be extended to one of for functions of bounded variation (BV). The natural setting for investigating the former case is finitely spectral operators, and for the latter, well-bounded operators. Some such conditions are well-established. If X is a reflexive space, both type of Extensions are assured; in fact if X contains an isomorphic copy of co, then every Operator T ?? L(X) that has a continuous functional calculus necessarily admits a Borel one. We show that if a space X has a predual, then also every operator T ?? L(X) with a continuous functional calculus admits a bounded Borel functional Calculus. In case a Banach space X either contains an isomorphic copy of co, or has a Predual, and T ?? L(X) is an operator with an AC functional calculus, we find that the existence of a decomposition of the identity of bounded variation for T is sufficient to ensure that the AC functional calculus may be extended to a BV functional calculus. We also consider operators defined by a linear map on interpolation families of Banach spaces [Xr, X???] (r???1), where for example Xp = lp, Lp[0,1] or Cp. We show that under certain uniform boundedness conditions, the possession of a BV functional calculus by operators on the spaces Xp, p ?? (r, ???), may be extrapolated to the corresponding operators on the spaces Xr and X???.

Thesis (Ph. D.)--University of Newcastle, 1972. / Includes bibliographical references (leaves 134-142). Also available online.

Thesis (Ph. D.)--University of Oregon, 2002. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 57-58). Also available for download via the World Wide Web; free to University of Oregon users. Address: http://wwwlib.umi.com/cr/uoregon/fullcit?p3055703.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Berlin, Freie Univ., Diss., 1999. / Dateiformat: zip, Dateien im PDF-Format. Computerdatei im Fernzugriff.

Berlin, Freie Univ., Diss., 1999. / Dateiformat: zip, Dateien im PDF-Format. Computerdatei im Fernzugriff.

Kaiserslautern, Univ., Diss., 1995. / Erscheinungsjahr an der Haupttitelstelle: 1995. Computerdatei im Fernzugriff.

Kaiserslautern, Univ., Diss., 1995. / Erscheinungsjahr an der Haupttitelstelle: 1995. Computerdatei im Fernzugriff.

Oldenburg, Universiẗat, Diss., 1999. / Dateiformat: zip, Dateien im PDF-Format.