caa a22 4500 386307725 CHVBK 20180307111535.0 cr unu---uuuuu 161130e198812 xx s 000 0 eng 10.1017/S1446788700031116 doi S1446788700031116 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700031116 Kluvánek Igor Centre for Mathematical Analysis, Australian National University P. O. Box 4, Canberra, ACT 2600, Australia Scalar operators and integration [Elektronische Daten] [Igor Kluvánek] The notion of a scalar operator on a Banach space, in the sense of N. Dunford, is widened so as to cover those operators which can be approximated in the operator norm by linear combinations of disjoint values of an additive and multiplicative operator valued set function, P, on an algebra of sets in a space Ω such that P(Ω) = I, subject to some conditions guaranteeing that this definition is unambiguous. An operator T turns out to be scalar in this sense, if and only if, there exists a (not necessarily bounded) Boolean algebra of bounded projections such that the Banach algebra of operators it generates is semisimple and contains T. Copyright © Australian Mathematical Society 1988 46 G 10 nationallicence 47 B 40 nationallicence 47 D 30 nationallicence 443 A 22 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 45/3(1988-12), 401-420 1446-7887 45:3<401 1988 45 JAZ https://doi.org/10.1017/S1446788700031116 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700031116 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kluvánek Igor Centre for Mathematical Analysis, Australian National University P. O. Box 4, Canberra, ACT 2600, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/3(1988-12), 401-420 1446-7887 45:3<401 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge