Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Similarity orbits and the range of the generalized derivation $ X\to MX-XN$


Author: Allen Schweinsberg
Journal: Trans. Amer. Math. Soc. 324 (1991), 201-211
MSC: Primary 47A65; Secondary 47B15, 47B47
DOI: https://doi.org/10.1090/S0002-9947-1991-1005938-1
MathSciNet review: 1005938
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ M$ and $ N$ are bounded operators on infinite dimensional complex Hilbert spaces $ \mathcal{H}$ and $ \mathcal{K}$, let $ \tau (X) = MX - XN$ for $ X$ in $ \mathcal{L}(\mathcal{K},\mathcal{H})$. The closure of the range of $ \tau$ is characterized when $ M$ and $ N$ are normal. There is a close connection between the range of $ \tau$ and operators $ C$ for which $ [\begin{array}{*{20}{c}} M \& C \\ 0 \& N \\ \end{array} ]$ is in the closure of the similarity orbit of $ [\begin{array}{*{20}{c}} M \& 0 \\ 0 ^ N \\ \end{array} ]$. This latter set is characterized and compared with the closure of the range of $ \tau$.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47A65, 47B15, 47B47

Retrieve articles in all journals with MSC: 47A65, 47B15, 47B47


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1991-1005938-1
Keywords: Rosenblum operators, Rosenblum's theorem, generalized derivations, similarity orbits
Article copyright: © Copyright 1991 American Mathematical Society