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On invertibility in non-selfadjoint operator algebras

Authors:	Junxi Zhao

Institution:	Department of Mathematics, Nanjing University, Nanjing 210008, People's Republic of China

Abstract:	Let $\mathcal {L}$ be a complete commutative subspace lattice on a Hilbert space. When $\mathcal {L}$ is purely atomic, we give a necessary and sufficient condition for $\sigma (T)= \sigma _{\mathcal {L}}(T)$ for every in $alg\mathcal {L}$ , where $\sigma _{\mathcal {L}}(T)$ and $\sigma (T)$ denote the spectrum of in $alg\mathcal {L}$ and respectively. In addition, we discuss the properties of the spectra and the invertibility conditions for operators in $alg\mathcal {L}$ .

Keywords:	Commutative subspace lattice spectrum

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