Geodesic
A noncommutative theory of Bade functionals
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 73-81

Voir la notice de l'article provenant de la source Cambridge University Press

Since the pioneering work of W. G. Bade [3, 4] a great deal of work has been done on bounded Boolean algebras of projections on a Banach space ([11, XVII.3.XVIII.3], [21, V.3], [16], [6], [12], [13], [14], ]17], [18], [23], [24]). Via the Stone representation space of the Boolean algebra, the theory can be studied through Banach modules over C(K), where K is a compact Hausdorff space. One of the key concepts in the theory is the notion of Bade functionals. If X is a Banach C(K)-module and x ε X, then a Bade functional of x with respect to C(K) is a continuous linear functional α on X such that, for each a in C(K) with a ≥ 0, we have(i) α (ax) ≥0,(ii) if α (ax) = 0, then ax = 0. 
Hadwin, Don; Orhon, Mehmet. A noncommutative theory of Bade functionals. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 73-81. doi: 10.1017/S0017089500008053
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