Norm conditions for uniform algebra isomorphisms

Aaron Luttman1, Scott Lambert2
1Bethany Lutheran College, Division of Science and Mathematics, Mankato, USA
2Department of Mathematical Sciences (MMAI01), University of Montana, Missoula, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Browder A., Introduction to function algebras, W.A. Benjamin Inc., New York-Amsterdam, 1969

Hatori O., Miura T., Takagi H., Characterization of isometric isomorphisms between uniform algebras via non-linear range preserving properties, Proc. Amer. Math. Soc., 2006, 134, 2923–2930

Hatori O., Miura T., Takagi H., Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative, J. Math. Anal. Appl., 2007, 326, 281–296

Hatori O., Miura T., Takagi H., Multiplicatively spectrum-preserving and norm-preserving maps between invertible groups of commutative Banach algebras, preprint

Hatori O., Miura T., Takagi H., Polynomially spectrum-preserving maps between commutative Banach algebras, preprint

Honma D., Surjections on the algebras of continuous functions which preserve peripheral spectrum, Contemp. Math., 2007, 435, 199–205

Honma D., Norm-preserving surjections on algbras of continuous functions, Rocky Mountain J. Math., to appear

Jiménez-Vargas A., Luttman A., Villegas-Vallecillos M., Weakly peripherally multiplicative surjections of pointed Lipschitz algebras, preprint

Kowalski S., Słodkowski Z., A Characterization of maximal ideals in commutative Banach algebras, Studia Math., 1980, 67, 215–223

Lambert S., Luttman A., Tonev T., Weakly peripherally-multiplicative operators between uniform algebras, Contemp. Math., 2007, 435, 265–281

Li C-K., Tsing N-K., Linear preserver problems: a brief introduction and some special techniques, Linear Algebra Appl., 1992, 162/164, 217–235

Luttman A., Tonev T., Uniform algebra isomorphisms and peripheral multiplicativity, Proc. Amer. Math. Soc., 2007, 135, 3589–3598

Mazur S., Ulam S., Sur les transformations isométriques d’espaces vectoriels normés, C. R. Math. Acad. Sci. Paris, 1932, 194, 946–948

Molnár L., Some characterizations of the automorphisms of B(H) and C(X), Proc. Amer. Math. Soc., 2001, 130, 111–120

Rao N.V., Roy A.K., Multiplicatively spectrum-preserving maps of function algebras, Proc. Amer. Math. Soc., 2005, 133, 1135–1142

Rao N.V., Roy A.K., Multiplicatively spectrum-preserving maps of function algebras II, Proc. Edinb. Math. Soc., 2005, 48, 219–229

Rao N.V., Tonev T., Toneva E., Uniform algebra isomorphisms and peripheral spectra, Contemp. Math., 2007, 427, 401–416