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A noncommutative theory of Bade functionals

Published online by Cambridge University Press:  18 May 2009

Don Hadwin  and
Mehmet Orhon
Don Hadwin
Affiliation:
Mathematics Department, University of New Hampshire, durham, NH 03824, U.S.A.
Mehmet Orhon
Affiliation:
Mathematics Department, Middle East Technical University, Ankara, Turkey
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 1 , January 1991 , pp. 73 - 81
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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