Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $alg\mathcal {L}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47D25

Retrieve articles in all journals with MSC (1991): 47D25

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

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

American Mathematical Society