 

Witold Majdak and
Laurian Suciu
Brownian isometric parts of concave operators
view
print


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


Abstract
We describe some invariant or reducing subspaces for a concave operator T on a complex Hilbert space which satisfies the regularity condition Δ_{T}T=Δ_{T}^{1/2}TΔ_{T}^{1/2}, where Δ_{T} = T*TI. We consider those subspaces on which T acts as a 2isometry 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 2isometry we determine the Brownian unitary reducing parts on which T has the maximal covariance. 

Acknowledgements
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
LBUSIRG201803.


Author information
Witold Majdak:
AGH University of Science and Technology
Faculty of Applied Mathematics
al. A. Mickiewicza 30, 30059 Krakow, Poland
majdak@agh.edu.pl
Laurian Suciu:
Department of Mathematics and Informatics
"Lucian Blaga" University of Sibiu, Romania
laurians2002@yahoo.com

