Convergence of functions of self-adjoint operators and applications

• Autores: Lawrence G. Brown
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 60, Nº 2, 2016, págs. 551-564
• Idioma: inglés
• DOI: 10.5565/10.5565-PUBLMAT_60216_09
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• Resumen

  • 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.