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Morita Equivalence of Nest Algebras

G. K. Eleftherakis

Abstract


Let $\mathscr{N}_1$ (resp. $\mathscr{N}_2$) be a nest, $A$ (resp. $B$) be the corresponding nest algebra, $A_0$ (resp. $B_0$) be the subalgebra of compact operators. We prove that the nests $\mathscr{N}_1, \mathscr{N}_2$ are isomorphic if and only if $A$ and $B$ are weakly-$*$ Morita equivalent if and only if $A_0$ and $ B_0$ are strongly Morita equivalent. We characterize the nest isomorphisms which implement stable isomorphism between the corresponding nest algebras.

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DOI: http://dx.doi.org/10.7146/math.scand.a-15483

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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