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The closure of unitary orbit for strongly irreducible operators in a class of nest algebras

Authors:

Institution:

(1) Institute of Math. of Fudan University, 200433 Shanghai, P.R.C.;(2) Dept. of Math. of Jilin University, 130023 Changchun, P.R.C.

Abstract:

A linear operatorT isin

L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let $\mathfrak{N}$ be a nest with infinite dimensional atoms, $\Gamma (\mathfrak{N})$ be the nest algebra associated with $\mathfrak{N}$ and $U(\mathfrak{N} \cap (SI))$ be the closure of $\left\{ {UTU^* \left| {T \in } \right.(SI) \cap \Gamma \left( \mathfrak{N} \right)} \right\}$ , then the following result is proved

$U\left( {\mathfrak{N} \cap \left( {SI} \right)} \right) = \left\{ {T\left| {T \in } \right.L\left( H \right),} \right.\sigma \left( T \right)is\left. {connected} \right\}.$

.The projection partially supported by Chinese Natural Science Foundation and Fund of Laboratory of Nonlinear Mathematical Modeling and Methods in Fudan University in Shanghai P.R.C.

Keywords:

AMS Classification Numbers" target="_blank">AMS Classification Numbers 47D25 47A58

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