A double commutant theorem for conjugate selfadjoint operators
HTML articles powered by AMS MathViewer
- by James W. Moeller
- Proc. Amer. Math. Soc. 83 (1981), 506-508
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627679-1
- PDF | Request permission
Abstract:
Let $A$ be a bounded linear transformation on the complex separable Hilbert space $H$. If there is a conjugation $Q$ on $H$ such that $A = Q{A^*}Q$, we say that $A$ is conjugate selfadjoint. In this note we examine commutativity properties of conjugate selfadjoint operators which possess cyclic vectors.References
- J. von Neumann, Über adjungierte Funktionaloperatoren, Ann. of Math. (2) 33 (1932), no. 2, 294–310 (German). MR 1503053, DOI 10.2307/1968331 M. Reed and B. Simon, Methods of modern mathematical physics. Vol. I: Functional analysis, Academic Press, New York, 1972.
- Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
- Harold Widom, Hankel matrices, Trans. Amer. Math. Soc. 121 (1966), 1–35. MR 187099, DOI 10.1090/S0002-9947-1966-0187099-X
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 506-508
- MSC: Primary 47B47; Secondary 47C05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627679-1
- MathSciNet review: 627679