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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On invertibility in non-selfadjoint
operator algebras


Author: Junxi Zhao
Journal: Proc. Amer. Math. Soc. 125 (1997), 101-109
MSC (1991): Primary 47D25
MathSciNet review: 1353409
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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 $T$ in $alg\mathcal {L}$, where $\sigma _{\mathcal {L}}(T)$ and $\sigma (T)$ denote the spectrum of $T$ in $alg\mathcal {L}$ and $B(H)$ respectively. In addition, we discuss the properties of the spectra and the invertibility conditions for operators in $alg\mathcal {L}$.


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Additional Information

Junxi Zhao
Affiliation: Department of Mathematics, Nanjing University, Nanjing 210008, People’s Republic of China
Address at time of publication: Post and Telecommunication Institute of Nanjing, Nanjing, 210003, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03645-9
PII: S 0002-9939(97)03645-9
Keywords: Commutative subspace lattice, spectrum
Received by editor(s): May 17, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society