Hermitian powers: A Müntz theorem and extremal algebras

M. J. Crabb, et al. "Hermitian powers: A Müntz theorem and extremal algebras." Studia Mathematica 146.1 (2001): 83-97. <http://eudml.org/doc/284716>.

@article{M2001,
abstract = {Given ⊂ ℕ, let ̂ be the set of all positive integers m for which $h^\{m\}$ is hermitian whenever h is an element of a complex unital Banach algebra A with hⁿ hermitian for each n ∈ . We attempt to characterize when (i) ̂ = ℕ, or (ii) ̂ = . A key tool is a Müntz-type theorem which gives remarkable conclusions when 1 ∈ and ∑ 1/n: n ∈ diverges. The set ̂ is determined by a single extremal Banach algebra Ea(). We describe this extremal algebra for various .},
author = {M. J. Crabb, J. Duncan, C. M. McGregor, T. J. Ransford},
journal = {Studia Mathematica},
keywords = {Hermitian powers; Müntz theorem; Vidav hermiticity; extremal algebras; self-adjointness; functional calculus; bounded linear operator; unital Banach algebra; Paley-Wiener theorem},
language = {eng},
number = {1},
pages = {83-97},
title = {Hermitian powers: A Müntz theorem and extremal algebras},
url = {http://eudml.org/doc/284716},
volume = {146},
year = {2001},
}

TY - JOUR
AU - M. J. Crabb
AU - J. Duncan
AU - C. M. McGregor
AU - T. J. Ransford
TI - Hermitian powers: A Müntz theorem and extremal algebras
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 1
SP - 83
EP - 97
AB - Given ⊂ ℕ, let ̂ be the set of all positive integers m for which $h^{m}$ is hermitian whenever h is an element of a complex unital Banach algebra A with hⁿ hermitian for each n ∈ . We attempt to characterize when (i) ̂ = ℕ, or (ii) ̂ = . A key tool is a Müntz-type theorem which gives remarkable conclusions when 1 ∈ and ∑ 1/n: n ∈ diverges. The set ̂ is determined by a single extremal Banach algebra Ea(). We describe this extremal algebra for various .
LA - eng
KW - Hermitian powers; Müntz theorem; Vidav hermiticity; extremal algebras; self-adjointness; functional calculus; bounded linear operator; unital Banach algebra; Paley-Wiener theorem
UR - http://eudml.org/doc/284716
ER -