We give several conditions for (A,m)-expansive operators to have the single-valued extension property. We also provide some spectral properties of such operators. Moreover, we prove that the A-covariance of any (A,2)-expansive operator T ∈ ℒ(ℋ ) is positive, showing that there exists a reducing subspace ℳ on which T is (A,2)-isometric. In addition, we verify that Weyl's theorem holds for an operator T ∈ ℒ(ℋ ) provided that T is (T*T,2)-expansive. We next study (A,m)-isometric operators as a special case of (A,m)-expansive operators. Finally, we prove that every operator T ∈ ℒ(ℋ ) which is (T*T,2)-isometric has a scalar extension.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-1-2,
author = {Sungeun Jung and Yoenha Kim and Eungil Ko and Ji Eun Lee},
title = {On (A,m)-expansive operators},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {3-23},
zbl = {1275.47037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-1-2}
}
Sungeun Jung; Yoenha Kim; Eungil Ko; Ji Eun Lee. On (A,m)-expansive operators. Studia Mathematica, Tome 209 (2012) pp. 3-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-1-2/