Our aim is to prove that for any fixed 1/2 < α < 1 there exists a Hilbert space contraction T such that σ(T) = 1 and . This answers Zemánek’s question on the time regularity property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-1, author = {Zolt\'an L\'eka}, title = {Time regularity and functions of the Volterra operator}, journal = {Studia Mathematica}, volume = {223}, year = {2014}, pages = {1-14}, zbl = {1285.47007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-1} }
Zoltán Léka. Time regularity and functions of the Volterra operator. Studia Mathematica, Tome 223 (2014) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-1/