1. CMB 2016 (vol 59 pp. 497)
||One-parameter Groups of Operators and Discrete Hilbert Transforms|
We show that the discrete Hilbert transform
and the discrete Kak-Hilbert transform
are infinitesimal generator of one-parameter groups of
operators in $\ell^2$.
Keywords:discrete Hilbert transform, groups of operators, isometries
Categories:42A45, 42A50, 41A44
2. CMB 2015 (vol 58 pp. 241)
||Isometries and Hermitian Operators on Zygmund Spaces|
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.
Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries
Categories:46E15, 47B15, 47B38
3. CMB 2010 (vol 53 pp. 398)
||Projections in the Convex Hull of Surjective Isometries|
We characterize those linear projections represented as a convex combination of two surjective isometries on standard Banach spaces of continuous functions with values in a strictly convex Banach space.
Keywords:isometry, convex combination of isometries, generalized bi-circular projections
Categories:47A65, 47B15, 47B37