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.
Published
2013-09-01
How to Cite
Eleftherakis, G. K. (2013). Morita Equivalence of Nest Algebras. MATHEMATICA SCANDINAVICA, 113(1), 83-107. https://doi.org/10.7146/math.scand.a-15483
Section
Articles