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On Unitary Equivalence of Matrices over the Ring of Continuous Complex-Valued Functions on a Stonian Space

Published online by Cambridge University Press:  20 November 2018

Carl Pearcy
Carl Pearcy*
Affiliation:
Humble Oil & Refining Company
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This paper is a continuation of the earlier papers (1, 5) in which the author studied matrices with entries from the algebra C() of all continuous, complex-valued functions on an extremely disconnected, compact Hausdorff space . (Such spaces are sometimes called Stonian, after M. H. Stone, who first considered them in (8). They arise naturally as maximal ideal spaces of abelian W*-algebras.) In this note, three theorems are proved.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 323 - 331
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Deckard, D. and Pearcy, C., On matrices over the ring of continuous complex-valued functions on a Stonian space, to appear in Proc. Amer. Math. Soc.Google Scholar
2. Dixmier, J., Les algèbres d'opérateurs dans Vespace hilbertien (Paris, 1957).Google Scholar
3. Kaplansky, I., Projections in Banach algebras, Ann. Math., 53 (1951), 235–249.Google Scholar
4. Kaplansky, I., Algebras of type I, Ann. Math., 56 (1952), 460–472.Google Scholar
5. Pearcy, C., A complete set of unitary invariants for operators generating finite W*-algebras of type I, to appear in Pacific J. Math.Google Scholar
6. Pearcy, C., A complete set of unitary invariants for 3X3 complex matrices, Trans. Amer. Math. Soc, 104 (1962), 425–429.Google Scholar
7. Specht, W., Zur Théorie der Matrizen II, Jahresber. Deutsch. Math. Verein., 50 (1940), 19–23.Google Scholar
8. Stone, M. H., Boundedness properties in function lattices, Can. J. Math., 1 (1949), 176–186.Google Scholar
9. Yen, T., Trace on finite AW*-algebras, Duke Math. J., 22 (1955), 207–222.Google Scholar