Weakly Compact Homomorphisms
Copyright policy )Weakly Compact Homomorphisms
The authors study weakly compact homomorphisms \(\theta\) from a Banach algebra \(A\) to a Banach algebra \(B\) and prove that under certain conditions on \(A\) and \(B\) the range of \(\theta\) is finite-dimensional and semisimple. It is so when \(A\) is a \(C^*\)-algebra, or when \(A\) is amenable, all irreducible representations of \(B\) are finite-dimensional and \(\theta(A)\) is dense in \(B\). Another result says that if \(A\) and \(B\) are commutative and \(A\) has a holomorphic structure, then every weakly compact \(\theta\) is compact.
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), finitely-dimensional, Topological algebras, normed rings and algebras, Banach algebras, Representations of topological algebras, \(C^*\)-algebra, Structure, classification of topological algebras, Homomorphisms and multipliers of function spaces on groups, semigroups, etc., General theory of \(C^*\)-algebras, Banach algebra, range, Linear operators defined by compactness properties, General theory of topological algebras, irreducible representations, weakly compact homomorphisms, holomorphic structure
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), finitely-dimensional, Topological algebras, normed rings and algebras, Banach algebras, Representations of topological algebras, \(C^*\)-algebra, Structure, classification of topological algebras, Homomorphisms and multipliers of function spaces on groups, semigroups, etc., General theory of \(C^*\)-algebras, Banach algebra, range, Linear operators defined by compactness properties, General theory of topological algebras, irreducible representations, weakly compact homomorphisms, holomorphic structure
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