Multidimensional weak resolvents and spatial equivalence of normal operators

Michał Jasiczak. "Multidimensional weak resolvents and spatial equivalence of normal operators." Studia Mathematica 173.2 (2006): 129-147. <http://eudml.org/doc/284698>.

@article{MichałJasiczak2006,
abstract = { The aim of this paper is to answer some questions concerning weak resolvents. Firstly, we investigate the domain of extension of weak resolvents Ω and find a formula linking Ω with the Taylor spectrum. We also show that equality of weak resolvents of operator tuples A and B results in isomorphism of the algebras generated by these operators. Although this isomorphism need not be of the form (1) X ↦ U*XU, where U is an isometry, for normal operators it is always possible to find a "large" subspace on which unitary similarity holds. This observation is used to prove that the infinite inflation of the spatial isomorphism between algebras generated by inflations of A and B, respectively, does have the form (1). These facts are generalized to other not necessarily commuting operators. We deal mostly with the self-adjoint case. },
author = {Michał Jasiczak},
journal = {Studia Mathematica},
keywords = {weak resolvent; spatial isomorphism; Taylor spectrum},
language = {eng},
number = {2},
pages = {129-147},
title = {Multidimensional weak resolvents and spatial equivalence of normal operators},
url = {http://eudml.org/doc/284698},
volume = {173},
year = {2006},
}

TY - JOUR
AU - Michał Jasiczak
TI - Multidimensional weak resolvents and spatial equivalence of normal operators
JO - Studia Mathematica
PY - 2006
VL - 173
IS - 2
SP - 129
EP - 147
AB - The aim of this paper is to answer some questions concerning weak resolvents. Firstly, we investigate the domain of extension of weak resolvents Ω and find a formula linking Ω with the Taylor spectrum. We also show that equality of weak resolvents of operator tuples A and B results in isomorphism of the algebras generated by these operators. Although this isomorphism need not be of the form (1) X ↦ U*XU, where U is an isometry, for normal operators it is always possible to find a "large" subspace on which unitary similarity holds. This observation is used to prove that the infinite inflation of the spatial isomorphism between algebras generated by inflations of A and B, respectively, does have the form (1). These facts are generalized to other not necessarily commuting operators. We deal mostly with the self-adjoint case.
LA - eng
KW - weak resolvent; spatial isomorphism; Taylor spectrum
UR - http://eudml.org/doc/284698
ER -