Closed densely defined operators commuting with multiplications in a multiplier pair
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- by Don Hadwin, Zhe Liu and Eric Nordgren PDF
- Proc. Amer. Math. Soc. 141 (2013), 3093-3105 Request permission
Abstract:
For a multiplier pair $\left ( X,Y\right )$ we study the closed densely defined operators $T$ on $X$ that commute with all of the multiplications by right multipliers in $X$. We apply our general results to special cases involving $H^{p}$, completions of $L^{\infty }\left [ 0,1\right ]$ with respect to certain norms, and the completion of a $II_{1}$ factor von Neumann algebra with respect to a unitarily invariant norm, where we show that each such $T$ is a “left multiplication”. However, we give an example of a closed densely defined operator on the Bergman space that commutes with all multiplications by $H^{\infty }$-functions but is not a multiplication operator.References
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Additional Information
- Don Hadwin
- Affiliation: Department of Mathematics, Kingsbury Hall, University of New Hampshire, Durham, New Hampshire 03824-3591
- Email: don@math.unh.edu
- Zhe Liu
- Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104
- MR Author ID: 959617
- Email: zheliu@sas.upenn.edu
- Eric Nordgren
- Affiliation: Department of Mathematics, Kingsbury Hall, University of New Hampshire, Durham, New Hampshire 03824-3591
- Email: ean@math.unh.edu
- Received by editor(s): November 11, 2011
- Published electronically: May 2, 2013
- Communicated by: Richard Rochberg
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3093-3105
- MSC (2010): Primary 46B99, 47B47; Secondary 30H10, 30H15, 46L10
- DOI: https://doi.org/10.1090/S0002-9939-2013-11753-3
- MathSciNet review: 3068963
Dedicated: Dedicated to the memory of Bill Arveson, an inspiration to us all