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The BochnerSchoenbergEberlein property and spectral synthesis for certain Banach algebra products


Eberhard Kaniuth,
Institut für Mathematik, Universität Paderborn, D33095 Paderborn, Germany
Abstract
Associated with two commutative Banach algebras $A$ and $B$ and
a character $\theta$ of $B$ is a certain Banach algebra product
$A\times_\theta B$, which is a splitting extension of $B$ by
$A$. We investigate two topics for the algebra $A\times_\theta
B$ in relation to the corresponding ones of $A$ and $B$. The
first one is the BochnerSchoenbergEberlein property and the
algebra of BochnerSchoenbergEberlein functions on the spectrum,
whereas the second one concerns the wide range of spectral synthesis
problems for $A\times_\theta B$.
Keywords: 
commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSEalgebra, BSEfunction
commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSEalgebra, BSEfunction

MSC Classifications: 
46J10, 46J25, 43A30, 43A45 show english descriptions
Banach algebras of continuous functions, function algebras [See also 46E25] Representations of commutative topological algebras Fourier and FourierStieltjes transforms on nonabelian groups and on semigroups, etc. Spectral synthesis on groups, semigroups, etc.
46J10  Banach algebras of continuous functions, function algebras [See also 46E25] 46J25  Representations of commutative topological algebras 43A30  Fourier and FourierStieltjes transforms on nonabelian groups and on semigroups, etc. 43A45  Spectral synthesis on groups, semigroups, etc.
