Integral equalities for functions of unbounded spectral operators in Banach spaces
Benedetto Silvestri
GDML_Books, (2009), p.

The work is dedicated to investigating a limiting procedure for extending “local” integral operator equalities to “global” ones in the sense explained below, and to applying it to obtaining generalizations of the Newton-Leibniz formula for operator-valued functions for a wide class of unbounded operators. The integral equalities considered have the form g(RF)fx(RF)dμ(x)=h(RF). (1) They involve functions of the kind Xxfx(RF)B(F), where X is a general locally compact space, F runs over a suitable class of Banach subspaces of a fixed complex Banach space G, in particular F = G. The integrals are with respect to a general complex Radon measure on X and the σ(B(F),F)-topology on B(F), where F is a suitable subset of B(F)*, the topological dual of B(F). RF is a possibly unbounded scalar type spectral operator in F such that σ(RF)σ(RG), and for all x ∈ X, fx and g,h are complex-valued Borelian maps on the spectrum σ(RG) of RG. If F ≠ G we call the integral equality (1) “local”, while if F = G we call it “global”.

EUDML-ID : urn:eudml:doc:286000
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm464-0-1,
     author = {Benedetto Silvestri},
     title = {Integral equalities for functions of unbounded spectral operators in Banach spaces},
     series = {GDML\_Books},
     year = {2009},
     zbl = {1235.47035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm464-0-1}
}
Benedetto Silvestri. Integral equalities for functions of unbounded spectral operators in Banach spaces. GDML_Books (2009),  http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm464-0-1/