New York Journal of Mathematics
Volume 25 (2019), 1067-1090


Witold Majdak and Laurian Suciu

Brownian isometric parts of concave operators

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Published: October 15, 2019.
Keywords: invariant (reducing) subspace, concave operator, Brownian unitary (isometric) operator, subbrownian operator.
Subject: 47A05 and 47A15.

We describe some invariant or reducing subspaces for a concave operator T on a complex Hilbert space which satisfies the regularity condition ΔTT=ΔT1/2T1/2, where ΔT = T*T-I. We consider those subspaces on which T acts as a 2-isometry and show that T has some Brownian type properties on them. Among other, the Brownian unitary part and the Brownian isometric (reducing or invariant) parts are investigated. In the case when T is a Brownian operator or even a general 2-isometry we determine the Brownian unitary reducing parts on which T has the maximal covariance.


The authors are grateful to the anonymous referee for his thorough reading of the manuscript and his very helpful comments which led to the improvement of the presentation. The second named author was supported by a Project financed from Lucian Blaga University of Sibiu research grants LBUS-IRG-2018-03.

Author information

Witold Majdak:
AGH University of Science and Technology
Faculty of Applied Mathematics
al. A. Mickiewicza 30, 30-059 Krakow, Poland


Laurian Suciu:
Department of Mathematics and Informatics
"Lucian Blaga" University of Sibiu, Romania