Continuity versus boundedness of the spectral factorization mapping

Holger Boche, and Volker Pohl. "Continuity versus boundedness of the spectral factorization mapping." Studia Mathematica 189.2 (2008): 131-145. <http://eudml.org/doc/284398>.

@article{HolgerBoche2008,
abstract = {This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.},
author = {Holger Boche, Volker Pohl},
journal = {Studia Mathematica},
keywords = {spectral factorization; boundedness; continuity; Riesz projection; nonlinear operators},
language = {eng},
number = {2},
pages = {131-145},
title = {Continuity versus boundedness of the spectral factorization mapping},
url = {http://eudml.org/doc/284398},
volume = {189},
year = {2008},
}

TY - JOUR
AU - Holger Boche
AU - Volker Pohl
TI - Continuity versus boundedness of the spectral factorization mapping
JO - Studia Mathematica
PY - 2008
VL - 189
IS - 2
SP - 131
EP - 145
AB - This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.
LA - eng
KW - spectral factorization; boundedness; continuity; Riesz projection; nonlinear operators
UR - http://eudml.org/doc/284398
ER -