Open Access
July 2017 The multiplier algebra of the noncommutative Schwartz space
Tomasz Ciaś, Krzysztof Piszczek
Banach J. Math. Anal. 11(3): 615-635 (July 2017). DOI: 10.1215/17358787-2017-0007


We describe the multiplier algebra of the noncommutative Schwartz space. This multiplier algebra can be seen as the largest -algebra of unbounded operators on a separable Hilbert space with the classical Schwartz space of rapidly decreasing functions as the domain. We show in particular that it is neither a Q-algebra nor m-convex. On the other hand, we prove that classical tools of functional analysis, for example, the closed graph theorem, the open mapping theorem, or the uniform boundedness principle, are still available.


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Tomasz Ciaś. Krzysztof Piszczek. "The multiplier algebra of the noncommutative Schwartz space." Banach J. Math. Anal. 11 (3) 615 - 635, July 2017.


Received: 19 July 2016; Accepted: 20 September 2016; Published: July 2017
First available in Project Euclid: 6 May 2017

zbMATH: 06754305
MathSciNet: MR3679898
Digital Object Identifier: 10.1215/17358787-2017-0007

Primary: 47L10
Secondary: 46A11 , 46A13 , 46H15 , 46K10

Keywords: $\mathrm{PLS}$-space , (Fréchet) $m$-convex algebra , (noncommutative) Schwartz space , multiplier algebra‎

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 3 • July 2017
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