On the Continuity of the Support of Bimodules over Maximal Abelian Self-Adjoint Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 93-95.

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We relate the convergence of a net of maximal Abelian selfadjoint algebras (masas) to that of the net of their corresponding supports. This is achieved by using a family of capacities on the collection of subsets of $X\times Y$ (where the masas are realized as collections of operators of multiplication by essentially bounded functions on the measure spaces $X$ and $Y$), which extends a capacity studied previously by Haydon and Shulman.
Keywords: capacity, maximal Abelian self-adjoint algebra.
Mots-clés : convergence, bimodule
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J. L. Habgood; I. G. Todorov. On the Continuity of the Support of Bimodules over Maximal Abelian Self-Adjoint Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 93-95. http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a12/

[1] W. B. Arveson, Ann. of Math. (2), 100 (1974), 433–532 | DOI | MR | Zbl

[2] J. A. Erdos, A. Katavolos, V. S. Shulman, J. Funct. Anal., 157:2 (1998), 554–587 | DOI | MR | Zbl

[3] R. G. Haydon, V. S. Shulman, Proc. Amer. Math. Soc., 124 (1996), 497–503 | DOI | MR | Zbl

[4] A. I. Loginov, V. S. Shulman, Izv. AN SSSR, 39:6 (1975), 1260–1273 | MR | Zbl

[5] V. S. Shulman, Funkts. analiz i ego pril., 23:2 (1989), 86–87 | MR

[6] V. S. Shulman, I. G. Todorov, J. Operator Theory, 52:2 (2004), 371–384 | MR | Zbl

[7] V. S. Shulman, L. Turowska, J. Funct. Anal., 209:2 (2004), 293–331 | DOI | MR | Zbl