Banach Journal of Mathematical Analysis

Norm-additive in modulus maps between function algebras

Juan J. Font and Maliheh Hosseini

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Abstract

The main purpose of this paper is to characterize norm-additive in modulus, not necessarily linear, maps defined between function algebras (not necessarily unital or uniformly closed). In fact, for function algebras $A$ and $B$ on locally compact Hausdorff spaces $X$ and $Y$, respectively, we study surjections $T, S:A\longrightarrow B$ satisfying $\||Tf|+|Sg|\|_Y= \||f|+|g|\|_X$ for all $f,g\in A$.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 2 (2014), 79-92.

Dates
First available in Project Euclid: 4 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1396640053

Digital Object Identifier
doi:10.15352/bjma/1396640053

Mathematical Reviews number (MathSciNet)
MR3189540

Zentralblatt MATH identifier
06285264

Subjects
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 47B38: Operators on function spaces (general) 47B33: Composition operators

Keywords
Norm-additive in modulus map function algebra Choquet boundary uniform algebra peaking function

Citation

Hosseini, Maliheh; Font, Juan J. Norm-additive in modulus maps between function algebras. Banach J. Math. Anal. 8 (2014), no. 2, 79--92. doi:10.15352/bjma/1396640053. https://projecteuclid.org/euclid.bjma/1396640053


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