A NONCOMMUTATIVE-THEORY OF BADE FUNCTIONALS

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1991-01-01

Author

HADWIN, D
ORHON, M

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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.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/65318

Journal

GLASGOW MATHEMATICAL JOURNAL

DOI

https://doi.org/10.1017/s0017089500008053

Collections

Department of Mathematics, Article

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Citation Formats

D. HADWIN and M. ORHON, “A NONCOMMUTATIVE-THEORY OF BADE FUNCTIONALS,” GLASGOW MATHEMATICAL JOURNAL, pp. 73–81, 1991, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65318.