Square functions, bounded analytic semigroups, and applications

Christian Le Merdy

Banach Center Publications, Tome 75 (2007), p. 191-220 / Harvested from The Polish Digital Mathematics Library

Résumé

To any bounded analytic semigroup on Hilbert space or on $L^{p}$ -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative $L^{p}$ -spaces, Banach lattices, and their subspaces. We give some applications to $H^{\infty}$ functional calculus, similarity problems, multiplier theory, and control theory.

Publié le : 2007-01-01

Zbl 1136.47027

EUDML-ID : urn:eudml:doc:282490

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-12,
     author = {Christian Le Merdy},
     title = {Square functions, bounded analytic semigroups, and applications},
     journal = {Banach Center Publications},
     volume = {75},
     year = {2007},
     pages = {191-220},
     zbl = {1136.47027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-12}
}

Christian Le Merdy. Square functions, bounded analytic semigroups, and applications. Banach Center Publications, Tome 75 (2007) pp. 191-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc75-0-12/