Convergence of functions of self-adjoint operators and applications
Brown, Lawrence G. (Purdue University. Department of Mathematics)

Data:	2016
Resum:	The main result (roughly) is that if Hi converges weakly to H and if also f (Hi) converges weakly to f(H), for a single strictly convex continuous function f, then (Hi) must converge strongly to H. One application is that if f(pr(H)) = pr(f(H)), where pr denotes compression to a closed subspace M, then M must be invariant for H. A consequence of this is the verification of a conjecture of Arveson, that Theorem 9. 4 of [Arv] remains true in the infinite dimensional case. And there are two applications to operator algebras. If h and f(h) are both quasimultipliers, then h must be a multiplier. Also (still roughly stated), if h and f(h) are both in pAsap, for a closed projection p, then h must be strongly q-continuous on p.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Self-adjoint operator ; Weak convergence ; Strong convergence ; Strictly convex function ; Korovkin type theorem ; Kaplansky density theorem ; Quasimultiplier ; Q-continuous
Publicat a:	Publicacions matemàtiques, Vol. 60 Núm. 2 (2016) , p. 551-564 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/311024
DOI: 10.5565/PUBLMAT_60216_09

14 p, 344.1 KB

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