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Regularity for Operator Algebras on a Hilbert Space
| Content Provider | Scilit |
|---|---|
| Author | Froelich, John |
| Copyright Year | 1993 |
| Description | Four notions of regularity for operator algebras are introduced. An algebra $A$ is called $1$-regular if for any two linearly independent vectors $x,y \in H$ there is an $a \in A$ such that $ax = 0$ and $ay \ne 0$. We show that the only weakly closed transitive $1$-regular algebra is $B(H)$, thus providing a natural generalization of the Rickart-Yood density theorem. We construct an example of a $1$-regular algebra which contains no nonzero compact operators. This example is related to the "thin set" phenomena of classical harmonic analysis. |
| Related Links | https://www.ams.org/proc/1993-119-04/S0002-9939-1993-1181164-8/S0002-9939-1993-1181164-8.pdf |
| Ending Page | 1277 |
| Page Count | 9 |
| Starting Page | 1269 |
| ISSN | 00029939 |
| e-ISSN | 10886826 |
| DOI | 10.2307/2159990 |
| Journal | Proceedings of the American Mathematical Society |
| Issue Number | 4 |
| Volume Number | 119 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1993-12-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Operator Algebras Regular Hilbert Theorem Weakly Notions Yood |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
