Separate and joint similarity to families of normal operators

Piotr Niemiec. "Separate and joint similarity to families of normal operators." Studia Mathematica 149.1 (2002): 39-62. <http://eudml.org/doc/284534>.

@article{PiotrNiemiec2002,
abstract = {Sets of bounded linear operators , ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that $G^\{-1\}··G = $. A bounded operator is scalar if it is similar to a normal operator. is jointly scalar if there exists a set ⊂ ℬ(H) of normal operators such that and are similar. is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented (Theorems 3.7, 4.4 and 4.6). Continuous algebra homomorphisms between the algebra of all complex-valued continuous functions on a compact Hausdorff space and the algebra of all bounded operators in a Hilbert space are studied.},
author = {Piotr Niemiec},
journal = {Studia Mathematica},
keywords = {normal operator; similarity; scalar operator; Hilbert space},
language = {eng},
number = {1},
pages = {39-62},
title = {Separate and joint similarity to families of normal operators},
url = {http://eudml.org/doc/284534},
volume = {149},
year = {2002},
}

TY - JOUR
AU - Piotr Niemiec
TI - Separate and joint similarity to families of normal operators
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 1
SP - 39
EP - 62
AB - Sets of bounded linear operators , ⊂ ℬ(H) (ℋ is a Hilbert space) are similar if there exists an invertible (in ℬ(H)) operator G such that $G^{-1}··G = $. A bounded operator is scalar if it is similar to a normal operator. is jointly scalar if there exists a set ⊂ ℬ(H) of normal operators such that and are similar. is separately scalar if all its elements are scalar. Some necessary and sufficient conditions for joint scalarity of a separately scalar abelian set of Hilbert space operators are presented (Theorems 3.7, 4.4 and 4.6). Continuous algebra homomorphisms between the algebra of all complex-valued continuous functions on a compact Hausdorff space and the algebra of all bounded operators in a Hilbert space are studied.
LA - eng
KW - normal operator; similarity; scalar operator; Hilbert space
UR - http://eudml.org/doc/284534
ER -