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Integral representation of multiplicative, involution preserving operators in ๐”(โ„ญโ‚€(๐”–,๐”„),๐”…)

Integral representation of multiplicative, involution preserving operators in ๐”(โ„ญโ‚€(๐”–,๐”„),๐”…)

Bounded linear operators from the space of continuous vector-valued functions which preserve multiplication and involution are characterized in terms of their representing measures. A key role is played by the Arens product in the second dual of a Banach algebra.