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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.
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 -