Finite operators
Author:
J. P. Williams
Journal:
Proc. Amer. Math. Soc. 26 (1970), 129-136
MSC:
Primary 47.40
DOI:
https://doi.org/10.1090/S0002-9939-1970-0264445-6
MathSciNet review:
0264445
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Abstract | References | Similar Articles | Additional Information
Abstract: A bounded linear operator $A$ on a Hilbert space $H$ is called finite if $||AX - XA - 1|| \geqq 1$ for each $X \in B(H)$. The class of finite operators is uniformly closed, contains every normal operator, every operator with a compact direct summand, and the entire ${C^ \ast }$-algebra generated by each of its members. These results imply that the set of operators with a finite dimensional reducing subspace is not uniformly dense. It is also shown that the set of self-commutators is uniformly closed.
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Additional Information
Keywords:
Commutators,
reducible operators,
numerical range,
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Article copyright:
© Copyright 1970
American Mathematical Society